01How Computers Work
Practice library / Eight-bit addition

Fully solved problem book

Eight-bit addition

Set 7 of 14 · 32 worked questions. Predict your result before expanding the solution.

These worked traces are meant to build fluency through controlled variation. If several answers feel identical, try the next difficult value and look for the point where a carry, sign, branch, or selected memory address changes the outcome.

Bitwise arithmetic · Problem 0193

Add 01110011₂ and 00011111₂; keep the low eight result bits.

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Use exactly eight bits: A=01110011, B=00011111.
  2. Ordinary decimal arithmetic gives 115+31=146.
  3. We process bits from the rightmost column (bit zero) to the leftmost (bit seven).
  4. Bit 0 (weight 1): 1+1+incoming carry 0=2; write 0, pass carry 1.
  5. Bit 1 (weight 2): 1+1+incoming carry 1=3; write 1, pass carry 1.
  6. Bit 2 (weight 4): 0+1+incoming carry 1=2; write 0, pass carry 1.
  7. Bit 3 (weight 8): 0+1+incoming carry 1=2; write 0, pass carry 1.
  8. Bit 4 (weight 16): 1+1+incoming carry 1=3; write 1, pass carry 1.
  9. Bit 5 (weight 32): 1+0+incoming carry 1=2; write 0, pass carry 1.
  10. Bit 6 (weight 64): 1+0+incoming carry 1=2; write 0, pass carry 1.
  11. Bit 7 (weight 128): 0+0+incoming carry 1=1; write 1, pass carry 0.
  12. The final carry-out is 0; it is outside the eight-bit result.
  13. The stored sum is 10010010, which is 146 unsigned.
  14. Check modular arithmetic: 146 modulo 256 = 146.
  15. Signed readings of the inputs are 115 and 31; signed overflow should be evaluated separately.
  16. An ALU may expose carry-out and signed overflow as different flags.

Final answer: 10010010

Bitwise arithmetic · Problem 0194

Add 01110011₂ and 11100110₂; keep the low eight result bits.

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Use exactly eight bits: A=01110011, B=11100110.
  2. Ordinary decimal arithmetic gives 115+230=345.
  3. We process bits from the rightmost column (bit zero) to the leftmost (bit seven).
  4. Bit 0 (weight 1): 1+0+incoming carry 0=1; write 1, pass carry 0.
  5. Bit 1 (weight 2): 1+1+incoming carry 0=2; write 0, pass carry 1.
  6. Bit 2 (weight 4): 0+1+incoming carry 1=2; write 0, pass carry 1.
  7. Bit 3 (weight 8): 0+0+incoming carry 1=1; write 1, pass carry 0.
  8. Bit 4 (weight 16): 1+0+incoming carry 0=1; write 1, pass carry 0.
  9. Bit 5 (weight 32): 1+1+incoming carry 0=2; write 0, pass carry 1.
  10. Bit 6 (weight 64): 1+1+incoming carry 1=3; write 1, pass carry 1.
  11. Bit 7 (weight 128): 0+1+incoming carry 1=2; write 0, pass carry 1.
  12. The final carry-out is 1; it is outside the eight-bit result.
  13. The stored sum is 01011001, which is 89 unsigned.
  14. Check modular arithmetic: 345 modulo 256 = 89.
  15. Signed readings of the inputs are 115 and -26; signed overflow should be evaluated separately.
  16. An ALU may expose carry-out and signed overflow as different flags.

Final answer: 01011001

Bitwise arithmetic · Problem 0195

Add 01110100₂ and 10111010₂; keep the low eight result bits.

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Use exactly eight bits: A=01110100, B=10111010.
  2. Ordinary decimal arithmetic gives 116+186=302.
  3. We process bits from the rightmost column (bit zero) to the leftmost (bit seven).
  4. Bit 0 (weight 1): 0+0+incoming carry 0=0; write 0, pass carry 0.
  5. Bit 1 (weight 2): 0+1+incoming carry 0=1; write 1, pass carry 0.
  6. Bit 2 (weight 4): 1+0+incoming carry 0=1; write 1, pass carry 0.
  7. Bit 3 (weight 8): 0+1+incoming carry 0=1; write 1, pass carry 0.
  8. Bit 4 (weight 16): 1+1+incoming carry 0=2; write 0, pass carry 1.
  9. Bit 5 (weight 32): 1+1+incoming carry 1=3; write 1, pass carry 1.
  10. Bit 6 (weight 64): 1+0+incoming carry 1=2; write 0, pass carry 1.
  11. Bit 7 (weight 128): 0+1+incoming carry 1=2; write 0, pass carry 1.
  12. The final carry-out is 1; it is outside the eight-bit result.
  13. The stored sum is 00101110, which is 46 unsigned.
  14. Check modular arithmetic: 302 modulo 256 = 46.
  15. Signed readings of the inputs are 116 and -70; signed overflow should be evaluated separately.
  16. An ALU may expose carry-out and signed overflow as different flags.

Final answer: 00101110

Bitwise arithmetic · Problem 0196

Add 01110100₂ and 11010011₂; keep the low eight result bits.

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Use exactly eight bits: A=01110100, B=11010011.
  2. Ordinary decimal arithmetic gives 116+211=327.
  3. We process bits from the rightmost column (bit zero) to the leftmost (bit seven).
  4. Bit 0 (weight 1): 0+1+incoming carry 0=1; write 1, pass carry 0.
  5. Bit 1 (weight 2): 0+1+incoming carry 0=1; write 1, pass carry 0.
  6. Bit 2 (weight 4): 1+0+incoming carry 0=1; write 1, pass carry 0.
  7. Bit 3 (weight 8): 0+0+incoming carry 0=0; write 0, pass carry 0.
  8. Bit 4 (weight 16): 1+1+incoming carry 0=2; write 0, pass carry 1.
  9. Bit 5 (weight 32): 1+0+incoming carry 1=2; write 0, pass carry 1.
  10. Bit 6 (weight 64): 1+1+incoming carry 1=3; write 1, pass carry 1.
  11. Bit 7 (weight 128): 0+1+incoming carry 1=2; write 0, pass carry 1.
  12. The final carry-out is 1; it is outside the eight-bit result.
  13. The stored sum is 01000111, which is 71 unsigned.
  14. Check modular arithmetic: 327 modulo 256 = 71.
  15. Signed readings of the inputs are 116 and -45; signed overflow should be evaluated separately.
  16. An ALU may expose carry-out and signed overflow as different flags.

Final answer: 01000111

Bitwise arithmetic · Problem 0197

Add 01110101₂ and 01001000₂; keep the low eight result bits.

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Use exactly eight bits: A=01110101, B=01001000.
  2. Ordinary decimal arithmetic gives 117+72=189.
  3. We process bits from the rightmost column (bit zero) to the leftmost (bit seven).
  4. Bit 0 (weight 1): 1+0+incoming carry 0=1; write 1, pass carry 0.
  5. Bit 1 (weight 2): 0+0+incoming carry 0=0; write 0, pass carry 0.
  6. Bit 2 (weight 4): 1+0+incoming carry 0=1; write 1, pass carry 0.
  7. Bit 3 (weight 8): 0+1+incoming carry 0=1; write 1, pass carry 0.
  8. Bit 4 (weight 16): 1+0+incoming carry 0=1; write 1, pass carry 0.
  9. Bit 5 (weight 32): 1+0+incoming carry 0=1; write 1, pass carry 0.
  10. Bit 6 (weight 64): 1+1+incoming carry 0=2; write 0, pass carry 1.
  11. Bit 7 (weight 128): 0+0+incoming carry 1=1; write 1, pass carry 0.
  12. The final carry-out is 0; it is outside the eight-bit result.
  13. The stored sum is 10111101, which is 189 unsigned.
  14. Check modular arithmetic: 189 modulo 256 = 189.
  15. Signed readings of the inputs are 117 and 72; signed overflow should be evaluated separately.
  16. An ALU may expose carry-out and signed overflow as different flags.

Final answer: 10111101

Bitwise arithmetic · Problem 0198

Add 01110101₂ and 10100011₂; keep the low eight result bits.

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Use exactly eight bits: A=01110101, B=10100011.
  2. Ordinary decimal arithmetic gives 117+163=280.
  3. We process bits from the rightmost column (bit zero) to the leftmost (bit seven).
  4. Bit 0 (weight 1): 1+1+incoming carry 0=2; write 0, pass carry 1.
  5. Bit 1 (weight 2): 0+1+incoming carry 1=2; write 0, pass carry 1.
  6. Bit 2 (weight 4): 1+0+incoming carry 1=2; write 0, pass carry 1.
  7. Bit 3 (weight 8): 0+0+incoming carry 1=1; write 1, pass carry 0.
  8. Bit 4 (weight 16): 1+0+incoming carry 0=1; write 1, pass carry 0.
  9. Bit 5 (weight 32): 1+1+incoming carry 0=2; write 0, pass carry 1.
  10. Bit 6 (weight 64): 1+0+incoming carry 1=2; write 0, pass carry 1.
  11. Bit 7 (weight 128): 0+1+incoming carry 1=2; write 0, pass carry 1.
  12. The final carry-out is 1; it is outside the eight-bit result.
  13. The stored sum is 00011000, which is 24 unsigned.
  14. Check modular arithmetic: 280 modulo 256 = 24.
  15. Signed readings of the inputs are 117 and -93; signed overflow should be evaluated separately.
  16. An ALU may expose carry-out and signed overflow as different flags.

Final answer: 00011000

Bitwise arithmetic · Problem 0199

Add 01110111₂ and 01101111₂; keep the low eight result bits.

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Use exactly eight bits: A=01110111, B=01101111.
  2. Ordinary decimal arithmetic gives 119+111=230.
  3. We process bits from the rightmost column (bit zero) to the leftmost (bit seven).
  4. Bit 0 (weight 1): 1+1+incoming carry 0=2; write 0, pass carry 1.
  5. Bit 1 (weight 2): 1+1+incoming carry 1=3; write 1, pass carry 1.
  6. Bit 2 (weight 4): 1+1+incoming carry 1=3; write 1, pass carry 1.
  7. Bit 3 (weight 8): 0+1+incoming carry 1=2; write 0, pass carry 1.
  8. Bit 4 (weight 16): 1+0+incoming carry 1=2; write 0, pass carry 1.
  9. Bit 5 (weight 32): 1+1+incoming carry 1=3; write 1, pass carry 1.
  10. Bit 6 (weight 64): 1+1+incoming carry 1=3; write 1, pass carry 1.
  11. Bit 7 (weight 128): 0+0+incoming carry 1=1; write 1, pass carry 0.
  12. The final carry-out is 0; it is outside the eight-bit result.
  13. The stored sum is 11100110, which is 230 unsigned.
  14. Check modular arithmetic: 230 modulo 256 = 230.
  15. Signed readings of the inputs are 119 and 111; signed overflow should be evaluated separately.
  16. An ALU may expose carry-out and signed overflow as different flags.

Final answer: 11100110

Bitwise arithmetic · Problem 0200

Add 01110111₂ and 10011110₂; keep the low eight result bits.

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Use exactly eight bits: A=01110111, B=10011110.
  2. Ordinary decimal arithmetic gives 119+158=277.
  3. We process bits from the rightmost column (bit zero) to the leftmost (bit seven).
  4. Bit 0 (weight 1): 1+0+incoming carry 0=1; write 1, pass carry 0.
  5. Bit 1 (weight 2): 1+1+incoming carry 0=2; write 0, pass carry 1.
  6. Bit 2 (weight 4): 1+1+incoming carry 1=3; write 1, pass carry 1.
  7. Bit 3 (weight 8): 0+1+incoming carry 1=2; write 0, pass carry 1.
  8. Bit 4 (weight 16): 1+1+incoming carry 1=3; write 1, pass carry 1.
  9. Bit 5 (weight 32): 1+0+incoming carry 1=2; write 0, pass carry 1.
  10. Bit 6 (weight 64): 1+0+incoming carry 1=2; write 0, pass carry 1.
  11. Bit 7 (weight 128): 0+1+incoming carry 1=2; write 0, pass carry 1.
  12. The final carry-out is 1; it is outside the eight-bit result.
  13. The stored sum is 00010101, which is 21 unsigned.
  14. Check modular arithmetic: 277 modulo 256 = 21.
  15. Signed readings of the inputs are 119 and -98; signed overflow should be evaluated separately.
  16. An ALU may expose carry-out and signed overflow as different flags.

Final answer: 00010101

Bitwise arithmetic · Problem 0201

Add 01110111₂ and 11110011₂; keep the low eight result bits.

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Use exactly eight bits: A=01110111, B=11110011.
  2. Ordinary decimal arithmetic gives 119+243=362.
  3. We process bits from the rightmost column (bit zero) to the leftmost (bit seven).
  4. Bit 0 (weight 1): 1+1+incoming carry 0=2; write 0, pass carry 1.
  5. Bit 1 (weight 2): 1+1+incoming carry 1=3; write 1, pass carry 1.
  6. Bit 2 (weight 4): 1+0+incoming carry 1=2; write 0, pass carry 1.
  7. Bit 3 (weight 8): 0+0+incoming carry 1=1; write 1, pass carry 0.
  8. Bit 4 (weight 16): 1+1+incoming carry 0=2; write 0, pass carry 1.
  9. Bit 5 (weight 32): 1+1+incoming carry 1=3; write 1, pass carry 1.
  10. Bit 6 (weight 64): 1+1+incoming carry 1=3; write 1, pass carry 1.
  11. Bit 7 (weight 128): 0+1+incoming carry 1=2; write 0, pass carry 1.
  12. The final carry-out is 1; it is outside the eight-bit result.
  13. The stored sum is 01101010, which is 106 unsigned.
  14. Check modular arithmetic: 362 modulo 256 = 106.
  15. Signed readings of the inputs are 119 and -13; signed overflow should be evaluated separately.
  16. An ALU may expose carry-out and signed overflow as different flags.

Final answer: 01101010

Bitwise arithmetic · Problem 0202

Add 01111001₂ and 00001011₂; keep the low eight result bits.

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Use exactly eight bits: A=01111001, B=00001011.
  2. Ordinary decimal arithmetic gives 121+11=132.
  3. We process bits from the rightmost column (bit zero) to the leftmost (bit seven).
  4. Bit 0 (weight 1): 1+1+incoming carry 0=2; write 0, pass carry 1.
  5. Bit 1 (weight 2): 0+1+incoming carry 1=2; write 0, pass carry 1.
  6. Bit 2 (weight 4): 0+0+incoming carry 1=1; write 1, pass carry 0.
  7. Bit 3 (weight 8): 1+1+incoming carry 0=2; write 0, pass carry 1.
  8. Bit 4 (weight 16): 1+0+incoming carry 1=2; write 0, pass carry 1.
  9. Bit 5 (weight 32): 1+0+incoming carry 1=2; write 0, pass carry 1.
  10. Bit 6 (weight 64): 1+0+incoming carry 1=2; write 0, pass carry 1.
  11. Bit 7 (weight 128): 0+0+incoming carry 1=1; write 1, pass carry 0.
  12. The final carry-out is 0; it is outside the eight-bit result.
  13. The stored sum is 10000100, which is 132 unsigned.
  14. Check modular arithmetic: 132 modulo 256 = 132.
  15. Signed readings of the inputs are 121 and 11; signed overflow should be evaluated separately.
  16. An ALU may expose carry-out and signed overflow as different flags.

Final answer: 10000100

Bitwise arithmetic · Problem 0203

Add 01111001₂ and 01011100₂; keep the low eight result bits.

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Use exactly eight bits: A=01111001, B=01011100.
  2. Ordinary decimal arithmetic gives 121+92=213.
  3. We process bits from the rightmost column (bit zero) to the leftmost (bit seven).
  4. Bit 0 (weight 1): 1+0+incoming carry 0=1; write 1, pass carry 0.
  5. Bit 1 (weight 2): 0+0+incoming carry 0=0; write 0, pass carry 0.
  6. Bit 2 (weight 4): 0+1+incoming carry 0=1; write 1, pass carry 0.
  7. Bit 3 (weight 8): 1+1+incoming carry 0=2; write 0, pass carry 1.
  8. Bit 4 (weight 16): 1+1+incoming carry 1=3; write 1, pass carry 1.
  9. Bit 5 (weight 32): 1+0+incoming carry 1=2; write 0, pass carry 1.
  10. Bit 6 (weight 64): 1+1+incoming carry 1=3; write 1, pass carry 1.
  11. Bit 7 (weight 128): 0+0+incoming carry 1=1; write 1, pass carry 0.
  12. The final carry-out is 0; it is outside the eight-bit result.
  13. The stored sum is 11010101, which is 213 unsigned.
  14. Check modular arithmetic: 213 modulo 256 = 213.
  15. Signed readings of the inputs are 121 and 92; signed overflow should be evaluated separately.
  16. An ALU may expose carry-out and signed overflow as different flags.

Final answer: 11010101

Bitwise arithmetic · Problem 0204

Add 01111010₂ and 10000001₂; keep the low eight result bits.

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Use exactly eight bits: A=01111010, B=10000001.
  2. Ordinary decimal arithmetic gives 122+129=251.
  3. We process bits from the rightmost column (bit zero) to the leftmost (bit seven).
  4. Bit 0 (weight 1): 0+1+incoming carry 0=1; write 1, pass carry 0.
  5. Bit 1 (weight 2): 1+0+incoming carry 0=1; write 1, pass carry 0.
  6. Bit 2 (weight 4): 0+0+incoming carry 0=0; write 0, pass carry 0.
  7. Bit 3 (weight 8): 1+0+incoming carry 0=1; write 1, pass carry 0.
  8. Bit 4 (weight 16): 1+0+incoming carry 0=1; write 1, pass carry 0.
  9. Bit 5 (weight 32): 1+0+incoming carry 0=1; write 1, pass carry 0.
  10. Bit 6 (weight 64): 1+0+incoming carry 0=1; write 1, pass carry 0.
  11. Bit 7 (weight 128): 0+1+incoming carry 0=1; write 1, pass carry 0.
  12. The final carry-out is 0; it is outside the eight-bit result.
  13. The stored sum is 11111011, which is 251 unsigned.
  14. Check modular arithmetic: 251 modulo 256 = 251.
  15. Signed readings of the inputs are 122 and -127; signed overflow should be evaluated separately.
  16. An ALU may expose carry-out and signed overflow as different flags.

Final answer: 11111011

Bitwise arithmetic · Problem 0205

Add 01111010₂ and 10010111₂; keep the low eight result bits.

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Use exactly eight bits: A=01111010, B=10010111.
  2. Ordinary decimal arithmetic gives 122+151=273.
  3. We process bits from the rightmost column (bit zero) to the leftmost (bit seven).
  4. Bit 0 (weight 1): 0+1+incoming carry 0=1; write 1, pass carry 0.
  5. Bit 1 (weight 2): 1+1+incoming carry 0=2; write 0, pass carry 1.
  6. Bit 2 (weight 4): 0+1+incoming carry 1=2; write 0, pass carry 1.
  7. Bit 3 (weight 8): 1+0+incoming carry 1=2; write 0, pass carry 1.
  8. Bit 4 (weight 16): 1+1+incoming carry 1=3; write 1, pass carry 1.
  9. Bit 5 (weight 32): 1+0+incoming carry 1=2; write 0, pass carry 1.
  10. Bit 6 (weight 64): 1+0+incoming carry 1=2; write 0, pass carry 1.
  11. Bit 7 (weight 128): 0+1+incoming carry 1=2; write 0, pass carry 1.
  12. The final carry-out is 1; it is outside the eight-bit result.
  13. The stored sum is 00010001, which is 17 unsigned.
  14. Check modular arithmetic: 273 modulo 256 = 17.
  15. Signed readings of the inputs are 122 and -105; signed overflow should be evaluated separately.
  16. An ALU may expose carry-out and signed overflow as different flags.

Final answer: 00010001

Bitwise arithmetic · Problem 0206

Add 01111011₂ and 00010001₂; keep the low eight result bits.

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Use exactly eight bits: A=01111011, B=00010001.
  2. Ordinary decimal arithmetic gives 123+17=140.
  3. We process bits from the rightmost column (bit zero) to the leftmost (bit seven).
  4. Bit 0 (weight 1): 1+1+incoming carry 0=2; write 0, pass carry 1.
  5. Bit 1 (weight 2): 1+0+incoming carry 1=2; write 0, pass carry 1.
  6. Bit 2 (weight 4): 0+0+incoming carry 1=1; write 1, pass carry 0.
  7. Bit 3 (weight 8): 1+0+incoming carry 0=1; write 1, pass carry 0.
  8. Bit 4 (weight 16): 1+1+incoming carry 0=2; write 0, pass carry 1.
  9. Bit 5 (weight 32): 1+0+incoming carry 1=2; write 0, pass carry 1.
  10. Bit 6 (weight 64): 1+0+incoming carry 1=2; write 0, pass carry 1.
  11. Bit 7 (weight 128): 0+0+incoming carry 1=1; write 1, pass carry 0.
  12. The final carry-out is 0; it is outside the eight-bit result.
  13. The stored sum is 10001100, which is 140 unsigned.
  14. Check modular arithmetic: 140 modulo 256 = 140.
  15. Signed readings of the inputs are 123 and 17; signed overflow should be evaluated separately.
  16. An ALU may expose carry-out and signed overflow as different flags.

Final answer: 10001100

Bitwise arithmetic · Problem 0207

Add 01111100₂ and 01100110₂; keep the low eight result bits.

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Use exactly eight bits: A=01111100, B=01100110.
  2. Ordinary decimal arithmetic gives 124+102=226.
  3. We process bits from the rightmost column (bit zero) to the leftmost (bit seven).
  4. Bit 0 (weight 1): 0+0+incoming carry 0=0; write 0, pass carry 0.
  5. Bit 1 (weight 2): 0+1+incoming carry 0=1; write 1, pass carry 0.
  6. Bit 2 (weight 4): 1+1+incoming carry 0=2; write 0, pass carry 1.
  7. Bit 3 (weight 8): 1+0+incoming carry 1=2; write 0, pass carry 1.
  8. Bit 4 (weight 16): 1+0+incoming carry 1=2; write 0, pass carry 1.
  9. Bit 5 (weight 32): 1+1+incoming carry 1=3; write 1, pass carry 1.
  10. Bit 6 (weight 64): 1+1+incoming carry 1=3; write 1, pass carry 1.
  11. Bit 7 (weight 128): 0+0+incoming carry 1=1; write 1, pass carry 0.
  12. The final carry-out is 0; it is outside the eight-bit result.
  13. The stored sum is 11100010, which is 226 unsigned.
  14. Check modular arithmetic: 226 modulo 256 = 226.
  15. Signed readings of the inputs are 124 and 102; signed overflow should be evaluated separately.
  16. An ALU may expose carry-out and signed overflow as different flags.

Final answer: 11100010

Bitwise arithmetic · Problem 0208

Add 01111101₂ and 10100001₂; keep the low eight result bits.

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Use exactly eight bits: A=01111101, B=10100001.
  2. Ordinary decimal arithmetic gives 125+161=286.
  3. We process bits from the rightmost column (bit zero) to the leftmost (bit seven).
  4. Bit 0 (weight 1): 1+1+incoming carry 0=2; write 0, pass carry 1.
  5. Bit 1 (weight 2): 0+0+incoming carry 1=1; write 1, pass carry 0.
  6. Bit 2 (weight 4): 1+0+incoming carry 0=1; write 1, pass carry 0.
  7. Bit 3 (weight 8): 1+0+incoming carry 0=1; write 1, pass carry 0.
  8. Bit 4 (weight 16): 1+0+incoming carry 0=1; write 1, pass carry 0.
  9. Bit 5 (weight 32): 1+1+incoming carry 0=2; write 0, pass carry 1.
  10. Bit 6 (weight 64): 1+0+incoming carry 1=2; write 0, pass carry 1.
  11. Bit 7 (weight 128): 0+1+incoming carry 1=2; write 0, pass carry 1.
  12. The final carry-out is 1; it is outside the eight-bit result.
  13. The stored sum is 00011110, which is 30 unsigned.
  14. Check modular arithmetic: 286 modulo 256 = 30.
  15. Signed readings of the inputs are 125 and -95; signed overflow should be evaluated separately.
  16. An ALU may expose carry-out and signed overflow as different flags.

Final answer: 00011110

Bitwise arithmetic · Problem 0209

Add 01111110₂ and 01000111₂; keep the low eight result bits.

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Use exactly eight bits: A=01111110, B=01000111.
  2. Ordinary decimal arithmetic gives 126+71=197.
  3. We process bits from the rightmost column (bit zero) to the leftmost (bit seven).
  4. Bit 0 (weight 1): 0+1+incoming carry 0=1; write 1, pass carry 0.
  5. Bit 1 (weight 2): 1+1+incoming carry 0=2; write 0, pass carry 1.
  6. Bit 2 (weight 4): 1+1+incoming carry 1=3; write 1, pass carry 1.
  7. Bit 3 (weight 8): 1+0+incoming carry 1=2; write 0, pass carry 1.
  8. Bit 4 (weight 16): 1+0+incoming carry 1=2; write 0, pass carry 1.
  9. Bit 5 (weight 32): 1+0+incoming carry 1=2; write 0, pass carry 1.
  10. Bit 6 (weight 64): 1+1+incoming carry 1=3; write 1, pass carry 1.
  11. Bit 7 (weight 128): 0+0+incoming carry 1=1; write 1, pass carry 0.
  12. The final carry-out is 0; it is outside the eight-bit result.
  13. The stored sum is 11000101, which is 197 unsigned.
  14. Check modular arithmetic: 197 modulo 256 = 197.
  15. Signed readings of the inputs are 126 and 71; signed overflow should be evaluated separately.
  16. An ALU may expose carry-out and signed overflow as different flags.

Final answer: 11000101

Bitwise arithmetic · Problem 0210

Add 01111110₂ and 01001011₂; keep the low eight result bits.

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Use exactly eight bits: A=01111110, B=01001011.
  2. Ordinary decimal arithmetic gives 126+75=201.
  3. We process bits from the rightmost column (bit zero) to the leftmost (bit seven).
  4. Bit 0 (weight 1): 0+1+incoming carry 0=1; write 1, pass carry 0.
  5. Bit 1 (weight 2): 1+1+incoming carry 0=2; write 0, pass carry 1.
  6. Bit 2 (weight 4): 1+0+incoming carry 1=2; write 0, pass carry 1.
  7. Bit 3 (weight 8): 1+1+incoming carry 1=3; write 1, pass carry 1.
  8. Bit 4 (weight 16): 1+0+incoming carry 1=2; write 0, pass carry 1.
  9. Bit 5 (weight 32): 1+0+incoming carry 1=2; write 0, pass carry 1.
  10. Bit 6 (weight 64): 1+1+incoming carry 1=3; write 1, pass carry 1.
  11. Bit 7 (weight 128): 0+0+incoming carry 1=1; write 1, pass carry 0.
  12. The final carry-out is 0; it is outside the eight-bit result.
  13. The stored sum is 11001001, which is 201 unsigned.
  14. Check modular arithmetic: 201 modulo 256 = 201.
  15. Signed readings of the inputs are 126 and 75; signed overflow should be evaluated separately.
  16. An ALU may expose carry-out and signed overflow as different flags.

Final answer: 11001001

Bitwise arithmetic · Problem 0211

Add 01111110₂ and 11101100₂; keep the low eight result bits.

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Use exactly eight bits: A=01111110, B=11101100.
  2. Ordinary decimal arithmetic gives 126+236=362.
  3. We process bits from the rightmost column (bit zero) to the leftmost (bit seven).
  4. Bit 0 (weight 1): 0+0+incoming carry 0=0; write 0, pass carry 0.
  5. Bit 1 (weight 2): 1+0+incoming carry 0=1; write 1, pass carry 0.
  6. Bit 2 (weight 4): 1+1+incoming carry 0=2; write 0, pass carry 1.
  7. Bit 3 (weight 8): 1+1+incoming carry 1=3; write 1, pass carry 1.
  8. Bit 4 (weight 16): 1+0+incoming carry 1=2; write 0, pass carry 1.
  9. Bit 5 (weight 32): 1+1+incoming carry 1=3; write 1, pass carry 1.
  10. Bit 6 (weight 64): 1+1+incoming carry 1=3; write 1, pass carry 1.
  11. Bit 7 (weight 128): 0+1+incoming carry 1=2; write 0, pass carry 1.
  12. The final carry-out is 1; it is outside the eight-bit result.
  13. The stored sum is 01101010, which is 106 unsigned.
  14. Check modular arithmetic: 362 modulo 256 = 106.
  15. Signed readings of the inputs are 126 and -20; signed overflow should be evaluated separately.
  16. An ALU may expose carry-out and signed overflow as different flags.

Final answer: 01101010

Bitwise arithmetic · Problem 0212

Add 01111110₂ and 11110000₂; keep the low eight result bits.

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Use exactly eight bits: A=01111110, B=11110000.
  2. Ordinary decimal arithmetic gives 126+240=366.
  3. We process bits from the rightmost column (bit zero) to the leftmost (bit seven).
  4. Bit 0 (weight 1): 0+0+incoming carry 0=0; write 0, pass carry 0.
  5. Bit 1 (weight 2): 1+0+incoming carry 0=1; write 1, pass carry 0.
  6. Bit 2 (weight 4): 1+0+incoming carry 0=1; write 1, pass carry 0.
  7. Bit 3 (weight 8): 1+0+incoming carry 0=1; write 1, pass carry 0.
  8. Bit 4 (weight 16): 1+1+incoming carry 0=2; write 0, pass carry 1.
  9. Bit 5 (weight 32): 1+1+incoming carry 1=3; write 1, pass carry 1.
  10. Bit 6 (weight 64): 1+1+incoming carry 1=3; write 1, pass carry 1.
  11. Bit 7 (weight 128): 0+1+incoming carry 1=2; write 0, pass carry 1.
  12. The final carry-out is 1; it is outside the eight-bit result.
  13. The stored sum is 01101110, which is 110 unsigned.
  14. Check modular arithmetic: 366 modulo 256 = 110.
  15. Signed readings of the inputs are 126 and -16; signed overflow should be evaluated separately.
  16. An ALU may expose carry-out and signed overflow as different flags.

Final answer: 01101110

Bitwise arithmetic · Problem 0213

Add 01111111₂ and 01010100₂; keep the low eight result bits.

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Use exactly eight bits: A=01111111, B=01010100.
  2. Ordinary decimal arithmetic gives 127+84=211.
  3. We process bits from the rightmost column (bit zero) to the leftmost (bit seven).
  4. Bit 0 (weight 1): 1+0+incoming carry 0=1; write 1, pass carry 0.
  5. Bit 1 (weight 2): 1+0+incoming carry 0=1; write 1, pass carry 0.
  6. Bit 2 (weight 4): 1+1+incoming carry 0=2; write 0, pass carry 1.
  7. Bit 3 (weight 8): 1+0+incoming carry 1=2; write 0, pass carry 1.
  8. Bit 4 (weight 16): 1+1+incoming carry 1=3; write 1, pass carry 1.
  9. Bit 5 (weight 32): 1+0+incoming carry 1=2; write 0, pass carry 1.
  10. Bit 6 (weight 64): 1+1+incoming carry 1=3; write 1, pass carry 1.
  11. Bit 7 (weight 128): 0+0+incoming carry 1=1; write 1, pass carry 0.
  12. The final carry-out is 0; it is outside the eight-bit result.
  13. The stored sum is 11010011, which is 211 unsigned.
  14. Check modular arithmetic: 211 modulo 256 = 211.
  15. Signed readings of the inputs are 127 and 84; signed overflow should be evaluated separately.
  16. An ALU may expose carry-out and signed overflow as different flags.

Final answer: 11010011

Bitwise arithmetic · Problem 0214

Add 01111111₂ and 10111011₂; keep the low eight result bits.

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Use exactly eight bits: A=01111111, B=10111011.
  2. Ordinary decimal arithmetic gives 127+187=314.
  3. We process bits from the rightmost column (bit zero) to the leftmost (bit seven).
  4. Bit 0 (weight 1): 1+1+incoming carry 0=2; write 0, pass carry 1.
  5. Bit 1 (weight 2): 1+1+incoming carry 1=3; write 1, pass carry 1.
  6. Bit 2 (weight 4): 1+0+incoming carry 1=2; write 0, pass carry 1.
  7. Bit 3 (weight 8): 1+1+incoming carry 1=3; write 1, pass carry 1.
  8. Bit 4 (weight 16): 1+1+incoming carry 1=3; write 1, pass carry 1.
  9. Bit 5 (weight 32): 1+1+incoming carry 1=3; write 1, pass carry 1.
  10. Bit 6 (weight 64): 1+0+incoming carry 1=2; write 0, pass carry 1.
  11. Bit 7 (weight 128): 0+1+incoming carry 1=2; write 0, pass carry 1.
  12. The final carry-out is 1; it is outside the eight-bit result.
  13. The stored sum is 00111010, which is 58 unsigned.
  14. Check modular arithmetic: 314 modulo 256 = 58.
  15. Signed readings of the inputs are 127 and -69; signed overflow should be evaluated separately.
  16. An ALU may expose carry-out and signed overflow as different flags.

Final answer: 00111010

Bitwise arithmetic · Problem 0215

Add 10000000₂ and 00111000₂; keep the low eight result bits.

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Use exactly eight bits: A=10000000, B=00111000.
  2. Ordinary decimal arithmetic gives 128+56=184.
  3. We process bits from the rightmost column (bit zero) to the leftmost (bit seven).
  4. Bit 0 (weight 1): 0+0+incoming carry 0=0; write 0, pass carry 0.
  5. Bit 1 (weight 2): 0+0+incoming carry 0=0; write 0, pass carry 0.
  6. Bit 2 (weight 4): 0+0+incoming carry 0=0; write 0, pass carry 0.
  7. Bit 3 (weight 8): 0+1+incoming carry 0=1; write 1, pass carry 0.
  8. Bit 4 (weight 16): 0+1+incoming carry 0=1; write 1, pass carry 0.
  9. Bit 5 (weight 32): 0+1+incoming carry 0=1; write 1, pass carry 0.
  10. Bit 6 (weight 64): 0+0+incoming carry 0=0; write 0, pass carry 0.
  11. Bit 7 (weight 128): 1+0+incoming carry 0=1; write 1, pass carry 0.
  12. The final carry-out is 0; it is outside the eight-bit result.
  13. The stored sum is 10111000, which is 184 unsigned.
  14. Check modular arithmetic: 184 modulo 256 = 184.
  15. Signed readings of the inputs are -128 and 56; signed overflow should be evaluated separately.
  16. An ALU may expose carry-out and signed overflow as different flags.

Final answer: 10111000

Bitwise arithmetic · Problem 0216

Add 10000010₂ and 00011101₂; keep the low eight result bits.

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Use exactly eight bits: A=10000010, B=00011101.
  2. Ordinary decimal arithmetic gives 130+29=159.
  3. We process bits from the rightmost column (bit zero) to the leftmost (bit seven).
  4. Bit 0 (weight 1): 0+1+incoming carry 0=1; write 1, pass carry 0.
  5. Bit 1 (weight 2): 1+0+incoming carry 0=1; write 1, pass carry 0.
  6. Bit 2 (weight 4): 0+1+incoming carry 0=1; write 1, pass carry 0.
  7. Bit 3 (weight 8): 0+1+incoming carry 0=1; write 1, pass carry 0.
  8. Bit 4 (weight 16): 0+1+incoming carry 0=1; write 1, pass carry 0.
  9. Bit 5 (weight 32): 0+0+incoming carry 0=0; write 0, pass carry 0.
  10. Bit 6 (weight 64): 0+0+incoming carry 0=0; write 0, pass carry 0.
  11. Bit 7 (weight 128): 1+0+incoming carry 0=1; write 1, pass carry 0.
  12. The final carry-out is 0; it is outside the eight-bit result.
  13. The stored sum is 10011111, which is 159 unsigned.
  14. Check modular arithmetic: 159 modulo 256 = 159.
  15. Signed readings of the inputs are -126 and 29; signed overflow should be evaluated separately.
  16. An ALU may expose carry-out and signed overflow as different flags.

Final answer: 10011111

Bitwise arithmetic · Problem 0217

Add 10000011₂ and 01100110₂; keep the low eight result bits.

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Use exactly eight bits: A=10000011, B=01100110.
  2. Ordinary decimal arithmetic gives 131+102=233.
  3. We process bits from the rightmost column (bit zero) to the leftmost (bit seven).
  4. Bit 0 (weight 1): 1+0+incoming carry 0=1; write 1, pass carry 0.
  5. Bit 1 (weight 2): 1+1+incoming carry 0=2; write 0, pass carry 1.
  6. Bit 2 (weight 4): 0+1+incoming carry 1=2; write 0, pass carry 1.
  7. Bit 3 (weight 8): 0+0+incoming carry 1=1; write 1, pass carry 0.
  8. Bit 4 (weight 16): 0+0+incoming carry 0=0; write 0, pass carry 0.
  9. Bit 5 (weight 32): 0+1+incoming carry 0=1; write 1, pass carry 0.
  10. Bit 6 (weight 64): 0+1+incoming carry 0=1; write 1, pass carry 0.
  11. Bit 7 (weight 128): 1+0+incoming carry 0=1; write 1, pass carry 0.
  12. The final carry-out is 0; it is outside the eight-bit result.
  13. The stored sum is 11101001, which is 233 unsigned.
  14. Check modular arithmetic: 233 modulo 256 = 233.
  15. Signed readings of the inputs are -125 and 102; signed overflow should be evaluated separately.
  16. An ALU may expose carry-out and signed overflow as different flags.

Final answer: 11101001

Bitwise arithmetic · Problem 0218

Add 10000100₂ and 00111000₂; keep the low eight result bits.

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Use exactly eight bits: A=10000100, B=00111000.
  2. Ordinary decimal arithmetic gives 132+56=188.
  3. We process bits from the rightmost column (bit zero) to the leftmost (bit seven).
  4. Bit 0 (weight 1): 0+0+incoming carry 0=0; write 0, pass carry 0.
  5. Bit 1 (weight 2): 0+0+incoming carry 0=0; write 0, pass carry 0.
  6. Bit 2 (weight 4): 1+0+incoming carry 0=1; write 1, pass carry 0.
  7. Bit 3 (weight 8): 0+1+incoming carry 0=1; write 1, pass carry 0.
  8. Bit 4 (weight 16): 0+1+incoming carry 0=1; write 1, pass carry 0.
  9. Bit 5 (weight 32): 0+1+incoming carry 0=1; write 1, pass carry 0.
  10. Bit 6 (weight 64): 0+0+incoming carry 0=0; write 0, pass carry 0.
  11. Bit 7 (weight 128): 1+0+incoming carry 0=1; write 1, pass carry 0.
  12. The final carry-out is 0; it is outside the eight-bit result.
  13. The stored sum is 10111100, which is 188 unsigned.
  14. Check modular arithmetic: 188 modulo 256 = 188.
  15. Signed readings of the inputs are -124 and 56; signed overflow should be evaluated separately.
  16. An ALU may expose carry-out and signed overflow as different flags.

Final answer: 10111100

Bitwise arithmetic · Problem 0219

Add 10000100₂ and 01001100₂; keep the low eight result bits.

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Use exactly eight bits: A=10000100, B=01001100.
  2. Ordinary decimal arithmetic gives 132+76=208.
  3. We process bits from the rightmost column (bit zero) to the leftmost (bit seven).
  4. Bit 0 (weight 1): 0+0+incoming carry 0=0; write 0, pass carry 0.
  5. Bit 1 (weight 2): 0+0+incoming carry 0=0; write 0, pass carry 0.
  6. Bit 2 (weight 4): 1+1+incoming carry 0=2; write 0, pass carry 1.
  7. Bit 3 (weight 8): 0+1+incoming carry 1=2; write 0, pass carry 1.
  8. Bit 4 (weight 16): 0+0+incoming carry 1=1; write 1, pass carry 0.
  9. Bit 5 (weight 32): 0+0+incoming carry 0=0; write 0, pass carry 0.
  10. Bit 6 (weight 64): 0+1+incoming carry 0=1; write 1, pass carry 0.
  11. Bit 7 (weight 128): 1+0+incoming carry 0=1; write 1, pass carry 0.
  12. The final carry-out is 0; it is outside the eight-bit result.
  13. The stored sum is 11010000, which is 208 unsigned.
  14. Check modular arithmetic: 208 modulo 256 = 208.
  15. Signed readings of the inputs are -124 and 76; signed overflow should be evaluated separately.
  16. An ALU may expose carry-out and signed overflow as different flags.

Final answer: 11010000

Bitwise arithmetic · Problem 0220

Add 10000101₂ and 10000111₂; keep the low eight result bits.

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Use exactly eight bits: A=10000101, B=10000111.
  2. Ordinary decimal arithmetic gives 133+135=268.
  3. We process bits from the rightmost column (bit zero) to the leftmost (bit seven).
  4. Bit 0 (weight 1): 1+1+incoming carry 0=2; write 0, pass carry 1.
  5. Bit 1 (weight 2): 0+1+incoming carry 1=2; write 0, pass carry 1.
  6. Bit 2 (weight 4): 1+1+incoming carry 1=3; write 1, pass carry 1.
  7. Bit 3 (weight 8): 0+0+incoming carry 1=1; write 1, pass carry 0.
  8. Bit 4 (weight 16): 0+0+incoming carry 0=0; write 0, pass carry 0.
  9. Bit 5 (weight 32): 0+0+incoming carry 0=0; write 0, pass carry 0.
  10. Bit 6 (weight 64): 0+0+incoming carry 0=0; write 0, pass carry 0.
  11. Bit 7 (weight 128): 1+1+incoming carry 0=2; write 0, pass carry 1.
  12. The final carry-out is 1; it is outside the eight-bit result.
  13. The stored sum is 00001100, which is 12 unsigned.
  14. Check modular arithmetic: 268 modulo 256 = 12.
  15. Signed readings of the inputs are -123 and -121; signed overflow should be evaluated separately.
  16. An ALU may expose carry-out and signed overflow as different flags.

Final answer: 00001100

Bitwise arithmetic · Problem 0221

Add 10000111₂ and 00101100₂; keep the low eight result bits.

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Use exactly eight bits: A=10000111, B=00101100.
  2. Ordinary decimal arithmetic gives 135+44=179.
  3. We process bits from the rightmost column (bit zero) to the leftmost (bit seven).
  4. Bit 0 (weight 1): 1+0+incoming carry 0=1; write 1, pass carry 0.
  5. Bit 1 (weight 2): 1+0+incoming carry 0=1; write 1, pass carry 0.
  6. Bit 2 (weight 4): 1+1+incoming carry 0=2; write 0, pass carry 1.
  7. Bit 3 (weight 8): 0+1+incoming carry 1=2; write 0, pass carry 1.
  8. Bit 4 (weight 16): 0+0+incoming carry 1=1; write 1, pass carry 0.
  9. Bit 5 (weight 32): 0+1+incoming carry 0=1; write 1, pass carry 0.
  10. Bit 6 (weight 64): 0+0+incoming carry 0=0; write 0, pass carry 0.
  11. Bit 7 (weight 128): 1+0+incoming carry 0=1; write 1, pass carry 0.
  12. The final carry-out is 0; it is outside the eight-bit result.
  13. The stored sum is 10110011, which is 179 unsigned.
  14. Check modular arithmetic: 179 modulo 256 = 179.
  15. Signed readings of the inputs are -121 and 44; signed overflow should be evaluated separately.
  16. An ALU may expose carry-out and signed overflow as different flags.

Final answer: 10110011

Bitwise arithmetic · Problem 0222

Add 10000111₂ and 01001010₂; keep the low eight result bits.

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Use exactly eight bits: A=10000111, B=01001010.
  2. Ordinary decimal arithmetic gives 135+74=209.
  3. We process bits from the rightmost column (bit zero) to the leftmost (bit seven).
  4. Bit 0 (weight 1): 1+0+incoming carry 0=1; write 1, pass carry 0.
  5. Bit 1 (weight 2): 1+1+incoming carry 0=2; write 0, pass carry 1.
  6. Bit 2 (weight 4): 1+0+incoming carry 1=2; write 0, pass carry 1.
  7. Bit 3 (weight 8): 0+1+incoming carry 1=2; write 0, pass carry 1.
  8. Bit 4 (weight 16): 0+0+incoming carry 1=1; write 1, pass carry 0.
  9. Bit 5 (weight 32): 0+0+incoming carry 0=0; write 0, pass carry 0.
  10. Bit 6 (weight 64): 0+1+incoming carry 0=1; write 1, pass carry 0.
  11. Bit 7 (weight 128): 1+0+incoming carry 0=1; write 1, pass carry 0.
  12. The final carry-out is 0; it is outside the eight-bit result.
  13. The stored sum is 11010001, which is 209 unsigned.
  14. Check modular arithmetic: 209 modulo 256 = 209.
  15. Signed readings of the inputs are -121 and 74; signed overflow should be evaluated separately.
  16. An ALU may expose carry-out and signed overflow as different flags.

Final answer: 11010001

Bitwise arithmetic · Problem 0223

Add 10000111₂ and 10110010₂; keep the low eight result bits.

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Use exactly eight bits: A=10000111, B=10110010.
  2. Ordinary decimal arithmetic gives 135+178=313.
  3. We process bits from the rightmost column (bit zero) to the leftmost (bit seven).
  4. Bit 0 (weight 1): 1+0+incoming carry 0=1; write 1, pass carry 0.
  5. Bit 1 (weight 2): 1+1+incoming carry 0=2; write 0, pass carry 1.
  6. Bit 2 (weight 4): 1+0+incoming carry 1=2; write 0, pass carry 1.
  7. Bit 3 (weight 8): 0+0+incoming carry 1=1; write 1, pass carry 0.
  8. Bit 4 (weight 16): 0+1+incoming carry 0=1; write 1, pass carry 0.
  9. Bit 5 (weight 32): 0+1+incoming carry 0=1; write 1, pass carry 0.
  10. Bit 6 (weight 64): 0+0+incoming carry 0=0; write 0, pass carry 0.
  11. Bit 7 (weight 128): 1+1+incoming carry 0=2; write 0, pass carry 1.
  12. The final carry-out is 1; it is outside the eight-bit result.
  13. The stored sum is 00111001, which is 57 unsigned.
  14. Check modular arithmetic: 313 modulo 256 = 57.
  15. Signed readings of the inputs are -121 and -78; signed overflow should be evaluated separately.
  16. An ALU may expose carry-out and signed overflow as different flags.

Final answer: 00111001

Bitwise arithmetic · Problem 0224

Add 10001000₂ and 01110011₂; keep the low eight result bits.

Try it on paper first. The worked answer is hidden below.

Reveal detailed solution →
  1. Use exactly eight bits: A=10001000, B=01110011.
  2. Ordinary decimal arithmetic gives 136+115=251.
  3. We process bits from the rightmost column (bit zero) to the leftmost (bit seven).
  4. Bit 0 (weight 1): 0+1+incoming carry 0=1; write 1, pass carry 0.
  5. Bit 1 (weight 2): 0+1+incoming carry 0=1; write 1, pass carry 0.
  6. Bit 2 (weight 4): 0+0+incoming carry 0=0; write 0, pass carry 0.
  7. Bit 3 (weight 8): 1+0+incoming carry 0=1; write 1, pass carry 0.
  8. Bit 4 (weight 16): 0+1+incoming carry 0=1; write 1, pass carry 0.
  9. Bit 5 (weight 32): 0+1+incoming carry 0=1; write 1, pass carry 0.
  10. Bit 6 (weight 64): 0+1+incoming carry 0=1; write 1, pass carry 0.
  11. Bit 7 (weight 128): 1+0+incoming carry 0=1; write 1, pass carry 0.
  12. The final carry-out is 0; it is outside the eight-bit result.
  13. The stored sum is 11111011, which is 251 unsigned.
  14. Check modular arithmetic: 251 modulo 256 = 251.
  15. Signed readings of the inputs are -120 and 115; signed overflow should be evaluated separately.
  16. An ALU may expose carry-out and signed overflow as different flags.

Final answer: 11111011