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Bitwise logic

Set 7 of 9 · 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.

Boolean logic · Problem 0193

Calculate 10101110 XOR 11001101.

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

Reveal detailed solution →
  1. A is the eight-bit string 10101110.
  2. B is the eight-bit string 11001101.
  3. The operation is XOR, applied separately to each matching bit position.
  4. Position 7 (weight 128): XOR(1, 1) = 0.
  5. Position 6 (weight 64): XOR(0, 1) = 1.
  6. Position 5 (weight 32): XOR(1, 0) = 1.
  7. Position 4 (weight 16): XOR(0, 0) = 0.
  8. Position 3 (weight 8): XOR(1, 1) = 0.
  9. Position 2 (weight 4): XOR(1, 1) = 0.
  10. Position 1 (weight 2): XOR(1, 0) = 1.
  11. Position 0 (weight 1): XOR(0, 1) = 1.
  12. Concatenate the output bits from position seven to zero: 01100011.
  13. The output is 99 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise XOR operation.

Final answer: 01100011

Boolean logic · Problem 0194

Calculate 10110001 AND 01101000.

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

Reveal detailed solution →
  1. A is the eight-bit string 10110001.
  2. B is the eight-bit string 01101000.
  3. The operation is AND, applied separately to each matching bit position.
  4. Position 7 (weight 128): AND(1, 0) = 0.
  5. Position 6 (weight 64): AND(0, 1) = 0.
  6. Position 5 (weight 32): AND(1, 1) = 1.
  7. Position 4 (weight 16): AND(1, 0) = 0.
  8. Position 3 (weight 8): AND(0, 1) = 0.
  9. Position 2 (weight 4): AND(0, 0) = 0.
  10. Position 1 (weight 2): AND(0, 0) = 0.
  11. Position 0 (weight 1): AND(1, 0) = 0.
  12. Concatenate the output bits from position seven to zero: 00100000.
  13. The output is 32 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise AND operation.

Final answer: 00100000

Boolean logic · Problem 0195

Calculate 10110010 OR 00000010.

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

Reveal detailed solution →
  1. A is the eight-bit string 10110010.
  2. B is the eight-bit string 00000010.
  3. The operation is OR, applied separately to each matching bit position.
  4. Position 7 (weight 128): OR(1, 0) = 1.
  5. Position 6 (weight 64): OR(0, 0) = 0.
  6. Position 5 (weight 32): OR(1, 0) = 1.
  7. Position 4 (weight 16): OR(1, 0) = 1.
  8. Position 3 (weight 8): OR(0, 0) = 0.
  9. Position 2 (weight 4): OR(0, 0) = 0.
  10. Position 1 (weight 2): OR(1, 1) = 1.
  11. Position 0 (weight 1): OR(0, 0) = 0.
  12. Concatenate the output bits from position seven to zero: 10110010.
  13. The output is 178 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise OR operation.

Final answer: 10110010

Boolean logic · Problem 0196

Calculate 10110011 AND 11010110.

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

Reveal detailed solution →
  1. A is the eight-bit string 10110011.
  2. B is the eight-bit string 11010110.
  3. The operation is AND, applied separately to each matching bit position.
  4. Position 7 (weight 128): AND(1, 1) = 1.
  5. Position 6 (weight 64): AND(0, 1) = 0.
  6. Position 5 (weight 32): AND(1, 0) = 0.
  7. Position 4 (weight 16): AND(1, 1) = 1.
  8. Position 3 (weight 8): AND(0, 0) = 0.
  9. Position 2 (weight 4): AND(0, 1) = 0.
  10. Position 1 (weight 2): AND(1, 1) = 1.
  11. Position 0 (weight 1): AND(1, 0) = 0.
  12. Concatenate the output bits from position seven to zero: 10010010.
  13. The output is 146 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise AND operation.

Final answer: 10010010

Boolean logic · Problem 0197

Calculate 10110100 XOR 01010111.

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

Reveal detailed solution →
  1. A is the eight-bit string 10110100.
  2. B is the eight-bit string 01010111.
  3. The operation is XOR, applied separately to each matching bit position.
  4. Position 7 (weight 128): XOR(1, 0) = 1.
  5. Position 6 (weight 64): XOR(0, 1) = 1.
  6. Position 5 (weight 32): XOR(1, 0) = 1.
  7. Position 4 (weight 16): XOR(1, 1) = 0.
  8. Position 3 (weight 8): XOR(0, 0) = 0.
  9. Position 2 (weight 4): XOR(1, 1) = 0.
  10. Position 1 (weight 2): XOR(0, 1) = 1.
  11. Position 0 (weight 1): XOR(0, 1) = 1.
  12. Concatenate the output bits from position seven to zero: 11100011.
  13. The output is 227 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise XOR operation.

Final answer: 11100011

Boolean logic · Problem 0198

Calculate 10110100 XOR 01101001.

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

Reveal detailed solution →
  1. A is the eight-bit string 10110100.
  2. B is the eight-bit string 01101001.
  3. The operation is XOR, applied separately to each matching bit position.
  4. Position 7 (weight 128): XOR(1, 0) = 1.
  5. Position 6 (weight 64): XOR(0, 1) = 1.
  6. Position 5 (weight 32): XOR(1, 1) = 0.
  7. Position 4 (weight 16): XOR(1, 0) = 1.
  8. Position 3 (weight 8): XOR(0, 1) = 1.
  9. Position 2 (weight 4): XOR(1, 0) = 1.
  10. Position 1 (weight 2): XOR(0, 0) = 0.
  11. Position 0 (weight 1): XOR(0, 1) = 1.
  12. Concatenate the output bits from position seven to zero: 11011101.
  13. The output is 221 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise XOR operation.

Final answer: 11011101

Boolean logic · Problem 0199

Calculate 10110101 AND 01101111.

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

Reveal detailed solution →
  1. A is the eight-bit string 10110101.
  2. B is the eight-bit string 01101111.
  3. The operation is AND, applied separately to each matching bit position.
  4. Position 7 (weight 128): AND(1, 0) = 0.
  5. Position 6 (weight 64): AND(0, 1) = 0.
  6. Position 5 (weight 32): AND(1, 1) = 1.
  7. Position 4 (weight 16): AND(1, 0) = 0.
  8. Position 3 (weight 8): AND(0, 1) = 0.
  9. Position 2 (weight 4): AND(1, 1) = 1.
  10. Position 1 (weight 2): AND(0, 1) = 0.
  11. Position 0 (weight 1): AND(1, 1) = 1.
  12. Concatenate the output bits from position seven to zero: 00100101.
  13. The output is 37 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise AND operation.

Final answer: 00100101

Boolean logic · Problem 0200

Calculate 10110101 XOR 01110010.

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

Reveal detailed solution →
  1. A is the eight-bit string 10110101.
  2. B is the eight-bit string 01110010.
  3. The operation is XOR, applied separately to each matching bit position.
  4. Position 7 (weight 128): XOR(1, 0) = 1.
  5. Position 6 (weight 64): XOR(0, 1) = 1.
  6. Position 5 (weight 32): XOR(1, 1) = 0.
  7. Position 4 (weight 16): XOR(1, 1) = 0.
  8. Position 3 (weight 8): XOR(0, 0) = 0.
  9. Position 2 (weight 4): XOR(1, 0) = 1.
  10. Position 1 (weight 2): XOR(0, 1) = 1.
  11. Position 0 (weight 1): XOR(1, 0) = 1.
  12. Concatenate the output bits from position seven to zero: 11000111.
  13. The output is 199 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise XOR operation.

Final answer: 11000111

Boolean logic · Problem 0201

Calculate 10110111 XOR 10101010.

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

Reveal detailed solution →
  1. A is the eight-bit string 10110111.
  2. B is the eight-bit string 10101010.
  3. The operation is XOR, applied separately to each matching bit position.
  4. Position 7 (weight 128): XOR(1, 1) = 0.
  5. Position 6 (weight 64): XOR(0, 0) = 0.
  6. Position 5 (weight 32): XOR(1, 1) = 0.
  7. Position 4 (weight 16): XOR(1, 0) = 1.
  8. Position 3 (weight 8): XOR(0, 1) = 1.
  9. Position 2 (weight 4): XOR(1, 0) = 1.
  10. Position 1 (weight 2): XOR(1, 1) = 0.
  11. Position 0 (weight 1): XOR(1, 0) = 1.
  12. Concatenate the output bits from position seven to zero: 00011101.
  13. The output is 29 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise XOR operation.

Final answer: 00011101

Boolean logic · Problem 0202

Calculate 10110111 XOR 11000010.

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

Reveal detailed solution →
  1. A is the eight-bit string 10110111.
  2. B is the eight-bit string 11000010.
  3. The operation is XOR, applied separately to each matching bit position.
  4. Position 7 (weight 128): XOR(1, 1) = 0.
  5. Position 6 (weight 64): XOR(0, 1) = 1.
  6. Position 5 (weight 32): XOR(1, 0) = 1.
  7. Position 4 (weight 16): XOR(1, 0) = 1.
  8. Position 3 (weight 8): XOR(0, 0) = 0.
  9. Position 2 (weight 4): XOR(1, 0) = 1.
  10. Position 1 (weight 2): XOR(1, 1) = 0.
  11. Position 0 (weight 1): XOR(1, 0) = 1.
  12. Concatenate the output bits from position seven to zero: 01110101.
  13. The output is 117 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise XOR operation.

Final answer: 01110101

Boolean logic · Problem 0203

Calculate 10110111 AND 11011100.

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

Reveal detailed solution →
  1. A is the eight-bit string 10110111.
  2. B is the eight-bit string 11011100.
  3. The operation is AND, applied separately to each matching bit position.
  4. Position 7 (weight 128): AND(1, 1) = 1.
  5. Position 6 (weight 64): AND(0, 1) = 0.
  6. Position 5 (weight 32): AND(1, 0) = 0.
  7. Position 4 (weight 16): AND(1, 1) = 1.
  8. Position 3 (weight 8): AND(0, 1) = 0.
  9. Position 2 (weight 4): AND(1, 1) = 1.
  10. Position 1 (weight 2): AND(1, 0) = 0.
  11. Position 0 (weight 1): AND(1, 0) = 0.
  12. Concatenate the output bits from position seven to zero: 10010100.
  13. The output is 148 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise AND operation.

Final answer: 10010100

Boolean logic · Problem 0204

Calculate 10111000 XOR 10100100.

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

Reveal detailed solution →
  1. A is the eight-bit string 10111000.
  2. B is the eight-bit string 10100100.
  3. The operation is XOR, applied separately to each matching bit position.
  4. Position 7 (weight 128): XOR(1, 1) = 0.
  5. Position 6 (weight 64): XOR(0, 0) = 0.
  6. Position 5 (weight 32): XOR(1, 1) = 0.
  7. Position 4 (weight 16): XOR(1, 0) = 1.
  8. Position 3 (weight 8): XOR(1, 0) = 1.
  9. Position 2 (weight 4): XOR(0, 1) = 1.
  10. Position 1 (weight 2): XOR(0, 0) = 0.
  11. Position 0 (weight 1): XOR(0, 0) = 0.
  12. Concatenate the output bits from position seven to zero: 00011100.
  13. The output is 28 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise XOR operation.

Final answer: 00011100

Boolean logic · Problem 0205

Calculate 10111010 AND 01110000.

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

Reveal detailed solution →
  1. A is the eight-bit string 10111010.
  2. B is the eight-bit string 01110000.
  3. The operation is AND, applied separately to each matching bit position.
  4. Position 7 (weight 128): AND(1, 0) = 0.
  5. Position 6 (weight 64): AND(0, 1) = 0.
  6. Position 5 (weight 32): AND(1, 1) = 1.
  7. Position 4 (weight 16): AND(1, 1) = 1.
  8. Position 3 (weight 8): AND(1, 0) = 0.
  9. Position 2 (weight 4): AND(0, 0) = 0.
  10. Position 1 (weight 2): AND(1, 0) = 0.
  11. Position 0 (weight 1): AND(0, 0) = 0.
  12. Concatenate the output bits from position seven to zero: 00110000.
  13. The output is 48 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise AND operation.

Final answer: 00110000

Boolean logic · Problem 0206

Calculate 10111100 AND 11110010.

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

Reveal detailed solution →
  1. A is the eight-bit string 10111100.
  2. B is the eight-bit string 11110010.
  3. The operation is AND, applied separately to each matching bit position.
  4. Position 7 (weight 128): AND(1, 1) = 1.
  5. Position 6 (weight 64): AND(0, 1) = 0.
  6. Position 5 (weight 32): AND(1, 1) = 1.
  7. Position 4 (weight 16): AND(1, 1) = 1.
  8. Position 3 (weight 8): AND(1, 0) = 0.
  9. Position 2 (weight 4): AND(1, 0) = 0.
  10. Position 1 (weight 2): AND(0, 1) = 0.
  11. Position 0 (weight 1): AND(0, 0) = 0.
  12. Concatenate the output bits from position seven to zero: 10110000.
  13. The output is 176 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise AND operation.

Final answer: 10110000

Boolean logic · Problem 0207

Calculate 10111110 OR 00000000.

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

Reveal detailed solution →
  1. A is the eight-bit string 10111110.
  2. B is the eight-bit string 00000000.
  3. The operation is OR, applied separately to each matching bit position.
  4. Position 7 (weight 128): OR(1, 0) = 1.
  5. Position 6 (weight 64): OR(0, 0) = 0.
  6. Position 5 (weight 32): OR(1, 0) = 1.
  7. Position 4 (weight 16): OR(1, 0) = 1.
  8. Position 3 (weight 8): OR(1, 0) = 1.
  9. Position 2 (weight 4): OR(1, 0) = 1.
  10. Position 1 (weight 2): OR(1, 0) = 1.
  11. Position 0 (weight 1): OR(0, 0) = 0.
  12. Concatenate the output bits from position seven to zero: 10111110.
  13. The output is 190 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise OR operation.

Final answer: 10111110

Boolean logic · Problem 0208

Calculate 11000000 AND 01000111.

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

Reveal detailed solution →
  1. A is the eight-bit string 11000000.
  2. B is the eight-bit string 01000111.
  3. The operation is AND, applied separately to each matching bit position.
  4. Position 7 (weight 128): AND(1, 0) = 0.
  5. Position 6 (weight 64): AND(1, 1) = 1.
  6. Position 5 (weight 32): AND(0, 0) = 0.
  7. Position 4 (weight 16): AND(0, 0) = 0.
  8. Position 3 (weight 8): AND(0, 0) = 0.
  9. Position 2 (weight 4): AND(0, 1) = 0.
  10. Position 1 (weight 2): AND(0, 1) = 0.
  11. Position 0 (weight 1): AND(0, 1) = 0.
  12. Concatenate the output bits from position seven to zero: 01000000.
  13. The output is 64 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise AND operation.

Final answer: 01000000

Boolean logic · Problem 0209

Calculate 11000000 AND 11100001.

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

Reveal detailed solution →
  1. A is the eight-bit string 11000000.
  2. B is the eight-bit string 11100001.
  3. The operation is AND, applied separately to each matching bit position.
  4. Position 7 (weight 128): AND(1, 1) = 1.
  5. Position 6 (weight 64): AND(1, 1) = 1.
  6. Position 5 (weight 32): AND(0, 1) = 0.
  7. Position 4 (weight 16): AND(0, 0) = 0.
  8. Position 3 (weight 8): AND(0, 0) = 0.
  9. Position 2 (weight 4): AND(0, 0) = 0.
  10. Position 1 (weight 2): AND(0, 0) = 0.
  11. Position 0 (weight 1): AND(0, 1) = 0.
  12. Concatenate the output bits from position seven to zero: 11000000.
  13. The output is 192 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise AND operation.

Final answer: 11000000

Boolean logic · Problem 0210

Calculate 11000011 AND 00101000.

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

Reveal detailed solution →
  1. A is the eight-bit string 11000011.
  2. B is the eight-bit string 00101000.
  3. The operation is AND, applied separately to each matching bit position.
  4. Position 7 (weight 128): AND(1, 0) = 0.
  5. Position 6 (weight 64): AND(1, 0) = 0.
  6. Position 5 (weight 32): AND(0, 1) = 0.
  7. Position 4 (weight 16): AND(0, 0) = 0.
  8. Position 3 (weight 8): AND(0, 1) = 0.
  9. Position 2 (weight 4): AND(0, 0) = 0.
  10. Position 1 (weight 2): AND(1, 0) = 0.
  11. Position 0 (weight 1): AND(1, 0) = 0.
  12. Concatenate the output bits from position seven to zero: 00000000.
  13. The output is 0 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise AND operation.

Final answer: 00000000

Boolean logic · Problem 0211

Calculate 11000011 AND 00111100.

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

Reveal detailed solution →
  1. A is the eight-bit string 11000011.
  2. B is the eight-bit string 00111100.
  3. The operation is AND, applied separately to each matching bit position.
  4. Position 7 (weight 128): AND(1, 0) = 0.
  5. Position 6 (weight 64): AND(1, 0) = 0.
  6. Position 5 (weight 32): AND(0, 1) = 0.
  7. Position 4 (weight 16): AND(0, 1) = 0.
  8. Position 3 (weight 8): AND(0, 1) = 0.
  9. Position 2 (weight 4): AND(0, 1) = 0.
  10. Position 1 (weight 2): AND(1, 0) = 0.
  11. Position 0 (weight 1): AND(1, 0) = 0.
  12. Concatenate the output bits from position seven to zero: 00000000.
  13. The output is 0 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise AND operation.

Final answer: 00000000

Boolean logic · Problem 0212

Calculate 11000100 XOR 00111110.

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

Reveal detailed solution →
  1. A is the eight-bit string 11000100.
  2. B is the eight-bit string 00111110.
  3. The operation is XOR, applied separately to each matching bit position.
  4. Position 7 (weight 128): XOR(1, 0) = 1.
  5. Position 6 (weight 64): XOR(1, 0) = 1.
  6. Position 5 (weight 32): XOR(0, 1) = 1.
  7. Position 4 (weight 16): XOR(0, 1) = 1.
  8. Position 3 (weight 8): XOR(0, 1) = 1.
  9. Position 2 (weight 4): XOR(1, 1) = 0.
  10. Position 1 (weight 2): XOR(0, 1) = 1.
  11. Position 0 (weight 1): XOR(0, 0) = 0.
  12. Concatenate the output bits from position seven to zero: 11111010.
  13. The output is 250 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise XOR operation.

Final answer: 11111010

Boolean logic · Problem 0213

Calculate 11000100 XOR 11010101.

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

Reveal detailed solution →
  1. A is the eight-bit string 11000100.
  2. B is the eight-bit string 11010101.
  3. The operation is XOR, applied separately to each matching bit position.
  4. Position 7 (weight 128): XOR(1, 1) = 0.
  5. Position 6 (weight 64): XOR(1, 1) = 0.
  6. Position 5 (weight 32): XOR(0, 0) = 0.
  7. Position 4 (weight 16): XOR(0, 1) = 1.
  8. Position 3 (weight 8): XOR(0, 0) = 0.
  9. Position 2 (weight 4): XOR(1, 1) = 0.
  10. Position 1 (weight 2): XOR(0, 0) = 0.
  11. Position 0 (weight 1): XOR(0, 1) = 1.
  12. Concatenate the output bits from position seven to zero: 00010001.
  13. The output is 17 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise XOR operation.

Final answer: 00010001

Boolean logic · Problem 0214

Calculate 11000100 XOR 11101101.

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

Reveal detailed solution →
  1. A is the eight-bit string 11000100.
  2. B is the eight-bit string 11101101.
  3. The operation is XOR, applied separately to each matching bit position.
  4. Position 7 (weight 128): XOR(1, 1) = 0.
  5. Position 6 (weight 64): XOR(1, 1) = 0.
  6. Position 5 (weight 32): XOR(0, 1) = 1.
  7. Position 4 (weight 16): XOR(0, 0) = 0.
  8. Position 3 (weight 8): XOR(0, 1) = 1.
  9. Position 2 (weight 4): XOR(1, 1) = 0.
  10. Position 1 (weight 2): XOR(0, 0) = 0.
  11. Position 0 (weight 1): XOR(0, 1) = 1.
  12. Concatenate the output bits from position seven to zero: 00101001.
  13. The output is 41 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise XOR operation.

Final answer: 00101001

Boolean logic · Problem 0215

Calculate 11000101 OR 01001110.

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

Reveal detailed solution →
  1. A is the eight-bit string 11000101.
  2. B is the eight-bit string 01001110.
  3. The operation is OR, applied separately to each matching bit position.
  4. Position 7 (weight 128): OR(1, 0) = 1.
  5. Position 6 (weight 64): OR(1, 1) = 1.
  6. Position 5 (weight 32): OR(0, 0) = 0.
  7. Position 4 (weight 16): OR(0, 0) = 0.
  8. Position 3 (weight 8): OR(0, 1) = 1.
  9. Position 2 (weight 4): OR(1, 1) = 1.
  10. Position 1 (weight 2): OR(0, 1) = 1.
  11. Position 0 (weight 1): OR(1, 0) = 1.
  12. Concatenate the output bits from position seven to zero: 11001111.
  13. The output is 207 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise OR operation.

Final answer: 11001111

Boolean logic · Problem 0216

Calculate 11001000 XOR 01011001.

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

Reveal detailed solution →
  1. A is the eight-bit string 11001000.
  2. B is the eight-bit string 01011001.
  3. The operation is XOR, applied separately to each matching bit position.
  4. Position 7 (weight 128): XOR(1, 0) = 1.
  5. Position 6 (weight 64): XOR(1, 1) = 0.
  6. Position 5 (weight 32): XOR(0, 0) = 0.
  7. Position 4 (weight 16): XOR(0, 1) = 1.
  8. Position 3 (weight 8): XOR(1, 1) = 0.
  9. Position 2 (weight 4): XOR(0, 0) = 0.
  10. Position 1 (weight 2): XOR(0, 0) = 0.
  11. Position 0 (weight 1): XOR(0, 1) = 1.
  12. Concatenate the output bits from position seven to zero: 10010001.
  13. The output is 145 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise XOR operation.

Final answer: 10010001

Boolean logic · Problem 0217

Calculate 11001010 AND 01011000.

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

Reveal detailed solution →
  1. A is the eight-bit string 11001010.
  2. B is the eight-bit string 01011000.
  3. The operation is AND, applied separately to each matching bit position.
  4. Position 7 (weight 128): AND(1, 0) = 0.
  5. Position 6 (weight 64): AND(1, 1) = 1.
  6. Position 5 (weight 32): AND(0, 0) = 0.
  7. Position 4 (weight 16): AND(0, 1) = 0.
  8. Position 3 (weight 8): AND(1, 1) = 1.
  9. Position 2 (weight 4): AND(0, 0) = 0.
  10. Position 1 (weight 2): AND(1, 0) = 0.
  11. Position 0 (weight 1): AND(0, 0) = 0.
  12. Concatenate the output bits from position seven to zero: 01001000.
  13. The output is 72 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise AND operation.

Final answer: 01001000

Boolean logic · Problem 0218

Calculate 11001011 XOR 10010000.

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

Reveal detailed solution →
  1. A is the eight-bit string 11001011.
  2. B is the eight-bit string 10010000.
  3. The operation is XOR, applied separately to each matching bit position.
  4. Position 7 (weight 128): XOR(1, 1) = 0.
  5. Position 6 (weight 64): XOR(1, 0) = 1.
  6. Position 5 (weight 32): XOR(0, 0) = 0.
  7. Position 4 (weight 16): XOR(0, 1) = 1.
  8. Position 3 (weight 8): XOR(1, 0) = 1.
  9. Position 2 (weight 4): XOR(0, 0) = 0.
  10. Position 1 (weight 2): XOR(1, 0) = 1.
  11. Position 0 (weight 1): XOR(1, 0) = 1.
  12. Concatenate the output bits from position seven to zero: 01011011.
  13. The output is 91 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise XOR operation.

Final answer: 01011011

Boolean logic · Problem 0219

Calculate 11001110 XOR 00011011.

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

Reveal detailed solution →
  1. A is the eight-bit string 11001110.
  2. B is the eight-bit string 00011011.
  3. The operation is XOR, applied separately to each matching bit position.
  4. Position 7 (weight 128): XOR(1, 0) = 1.
  5. Position 6 (weight 64): XOR(1, 0) = 1.
  6. Position 5 (weight 32): XOR(0, 0) = 0.
  7. Position 4 (weight 16): XOR(0, 1) = 1.
  8. Position 3 (weight 8): XOR(1, 1) = 0.
  9. Position 2 (weight 4): XOR(1, 0) = 1.
  10. Position 1 (weight 2): XOR(1, 1) = 0.
  11. Position 0 (weight 1): XOR(0, 1) = 1.
  12. Concatenate the output bits from position seven to zero: 11010101.
  13. The output is 213 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise XOR operation.

Final answer: 11010101

Boolean logic · Problem 0220

Calculate 11001110 OR 10100101.

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

Reveal detailed solution →
  1. A is the eight-bit string 11001110.
  2. B is the eight-bit string 10100101.
  3. The operation is OR, applied separately to each matching bit position.
  4. Position 7 (weight 128): OR(1, 1) = 1.
  5. Position 6 (weight 64): OR(1, 0) = 1.
  6. Position 5 (weight 32): OR(0, 1) = 1.
  7. Position 4 (weight 16): OR(0, 0) = 0.
  8. Position 3 (weight 8): OR(1, 0) = 1.
  9. Position 2 (weight 4): OR(1, 1) = 1.
  10. Position 1 (weight 2): OR(1, 0) = 1.
  11. Position 0 (weight 1): OR(0, 1) = 1.
  12. Concatenate the output bits from position seven to zero: 11101111.
  13. The output is 239 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise OR operation.

Final answer: 11101111

Boolean logic · Problem 0221

Calculate 11001110 XOR 11100110.

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

Reveal detailed solution →
  1. A is the eight-bit string 11001110.
  2. B is the eight-bit string 11100110.
  3. The operation is XOR, applied separately to each matching bit position.
  4. Position 7 (weight 128): XOR(1, 1) = 0.
  5. Position 6 (weight 64): XOR(1, 1) = 0.
  6. Position 5 (weight 32): XOR(0, 1) = 1.
  7. Position 4 (weight 16): XOR(0, 0) = 0.
  8. Position 3 (weight 8): XOR(1, 0) = 1.
  9. Position 2 (weight 4): XOR(1, 1) = 0.
  10. Position 1 (weight 2): XOR(1, 1) = 0.
  11. Position 0 (weight 1): XOR(0, 0) = 0.
  12. Concatenate the output bits from position seven to zero: 00101000.
  13. The output is 40 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise XOR operation.

Final answer: 00101000

Boolean logic · Problem 0222

Calculate 11010000 XOR 00110000.

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

Reveal detailed solution →
  1. A is the eight-bit string 11010000.
  2. B is the eight-bit string 00110000.
  3. The operation is XOR, applied separately to each matching bit position.
  4. Position 7 (weight 128): XOR(1, 0) = 1.
  5. Position 6 (weight 64): XOR(1, 0) = 1.
  6. Position 5 (weight 32): XOR(0, 1) = 1.
  7. Position 4 (weight 16): XOR(1, 1) = 0.
  8. Position 3 (weight 8): XOR(0, 0) = 0.
  9. Position 2 (weight 4): XOR(0, 0) = 0.
  10. Position 1 (weight 2): XOR(0, 0) = 0.
  11. Position 0 (weight 1): XOR(0, 0) = 0.
  12. Concatenate the output bits from position seven to zero: 11100000.
  13. The output is 224 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise XOR operation.

Final answer: 11100000

Boolean logic · Problem 0223

Calculate 11010000 OR 10101110.

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

Reveal detailed solution →
  1. A is the eight-bit string 11010000.
  2. B is the eight-bit string 10101110.
  3. The operation is OR, applied separately to each matching bit position.
  4. Position 7 (weight 128): OR(1, 1) = 1.
  5. Position 6 (weight 64): OR(1, 0) = 1.
  6. Position 5 (weight 32): OR(0, 1) = 1.
  7. Position 4 (weight 16): OR(1, 0) = 1.
  8. Position 3 (weight 8): OR(0, 1) = 1.
  9. Position 2 (weight 4): OR(0, 1) = 1.
  10. Position 1 (weight 2): OR(0, 1) = 1.
  11. Position 0 (weight 1): OR(0, 0) = 0.
  12. Concatenate the output bits from position seven to zero: 11111110.
  13. The output is 254 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise OR operation.

Final answer: 11111110

Boolean logic · Problem 0224

Calculate 11010001 XOR 10010001.

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

Reveal detailed solution →
  1. A is the eight-bit string 11010001.
  2. B is the eight-bit string 10010001.
  3. The operation is XOR, applied separately to each matching bit position.
  4. Position 7 (weight 128): XOR(1, 1) = 0.
  5. Position 6 (weight 64): XOR(1, 0) = 1.
  6. Position 5 (weight 32): XOR(0, 0) = 0.
  7. Position 4 (weight 16): XOR(1, 1) = 0.
  8. Position 3 (weight 8): XOR(0, 0) = 0.
  9. Position 2 (weight 4): XOR(0, 0) = 0.
  10. Position 1 (weight 2): XOR(0, 0) = 0.
  11. Position 0 (weight 1): XOR(1, 1) = 0.
  12. Concatenate the output bits from position seven to zero: 01000000.
  13. The output is 64 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise XOR operation.

Final answer: 01000000