01How Computers Work
Practice library / Bitwise logic

Fully solved problem book

Bitwise logic

Set 2 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 0033

Calculate 00011110 OR 00011110.

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

Reveal detailed solution →
  1. A is the eight-bit string 00011110.
  2. B is the eight-bit string 00011110.
  3. The operation is OR, applied separately to each matching bit position.
  4. Position 7 (weight 128): OR(0, 0) = 0.
  5. Position 6 (weight 64): OR(0, 0) = 0.
  6. Position 5 (weight 32): OR(0, 0) = 0.
  7. Position 4 (weight 16): OR(1, 1) = 1.
  8. Position 3 (weight 8): OR(1, 1) = 1.
  9. Position 2 (weight 4): OR(1, 1) = 1.
  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: 00011110.
  13. The output is 30 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise OR operation.

Final answer: 00011110

Boolean logic · Problem 0034

Calculate 00011110 AND 11110100.

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

Reveal detailed solution →
  1. A is the eight-bit string 00011110.
  2. B is the eight-bit string 11110100.
  3. The operation is AND, applied separately to each matching bit position.
  4. Position 7 (weight 128): AND(0, 1) = 0.
  5. Position 6 (weight 64): AND(0, 1) = 0.
  6. Position 5 (weight 32): AND(0, 1) = 0.
  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, 1) = 1.
  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: 00010100.
  13. The output is 20 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise AND operation.

Final answer: 00010100

Boolean logic · Problem 0035

Calculate 00100000 XOR 01101101.

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

Reveal detailed solution →
  1. A is the eight-bit string 00100000.
  2. B is the eight-bit string 01101101.
  3. The operation is XOR, applied separately to each matching bit position.
  4. Position 7 (weight 128): XOR(0, 0) = 0.
  5. Position 6 (weight 64): XOR(0, 1) = 1.
  6. Position 5 (weight 32): XOR(1, 1) = 0.
  7. Position 4 (weight 16): XOR(0, 0) = 0.
  8. Position 3 (weight 8): XOR(0, 1) = 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, 1) = 1.
  12. Concatenate the output bits from position seven to zero: 01001101.
  13. The output is 77 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise XOR operation.

Final answer: 01001101

Boolean logic · Problem 0036

Calculate 00100000 XOR 11011000.

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

Reveal detailed solution →
  1. A is the eight-bit string 00100000.
  2. B is the eight-bit string 11011000.
  3. The operation is XOR, applied separately to each matching bit position.
  4. Position 7 (weight 128): XOR(0, 1) = 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(0, 1) = 1.
  8. Position 3 (weight 8): XOR(0, 1) = 1.
  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: 11111000.
  13. The output is 248 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise XOR operation.

Final answer: 11111000

Boolean logic · Problem 0037

Calculate 00100001 OR 11111111.

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

Reveal detailed solution →
  1. A is the eight-bit string 00100001.
  2. B is the eight-bit string 11111111.
  3. The operation is OR, applied separately to each matching bit position.
  4. Position 7 (weight 128): OR(0, 1) = 1.
  5. Position 6 (weight 64): OR(0, 1) = 1.
  6. Position 5 (weight 32): OR(1, 1) = 1.
  7. Position 4 (weight 16): OR(0, 1) = 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(1, 1) = 1.
  12. Concatenate the output bits from position seven to zero: 11111111.
  13. The output is 255 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise OR operation.

Final answer: 11111111

Boolean logic · Problem 0038

Calculate 00100011 OR 11011101.

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

Reveal detailed solution →
  1. A is the eight-bit string 00100011.
  2. B is the eight-bit string 11011101.
  3. The operation is OR, applied separately to each matching bit position.
  4. Position 7 (weight 128): OR(0, 1) = 1.
  5. Position 6 (weight 64): OR(0, 1) = 1.
  6. Position 5 (weight 32): OR(1, 0) = 1.
  7. Position 4 (weight 16): OR(0, 1) = 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(1, 0) = 1.
  11. Position 0 (weight 1): OR(1, 1) = 1.
  12. Concatenate the output bits from position seven to zero: 11111111.
  13. The output is 255 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise OR operation.

Final answer: 11111111

Boolean logic · Problem 0039

Calculate 00100100 XOR 00011010.

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

Reveal detailed solution →
  1. A is the eight-bit string 00100100.
  2. B is the eight-bit string 00011010.
  3. The operation is XOR, applied separately to each matching bit position.
  4. Position 7 (weight 128): XOR(0, 0) = 0.
  5. Position 6 (weight 64): XOR(0, 0) = 0.
  6. Position 5 (weight 32): XOR(1, 0) = 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, 0) = 1.
  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: 00111110.
  13. The output is 62 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise XOR operation.

Final answer: 00111110

Boolean logic · Problem 0040

Calculate 00100100 XOR 11101100.

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

Reveal detailed solution →
  1. A is the eight-bit string 00100100.
  2. B is the eight-bit string 11101100.
  3. The operation is XOR, applied separately to each matching bit position.
  4. Position 7 (weight 128): XOR(0, 1) = 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(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, 0) = 0.
  12. Concatenate the output bits from position seven to zero: 11001000.
  13. The output is 200 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise XOR operation.

Final answer: 11001000

Boolean logic · Problem 0041

Calculate 00100101 XOR 11111110.

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

Reveal detailed solution →
  1. A is the eight-bit string 00100101.
  2. B is the eight-bit string 11111110.
  3. The operation is XOR, applied separately to each matching bit position.
  4. Position 7 (weight 128): XOR(0, 1) = 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(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(1, 0) = 1.
  12. Concatenate the output bits from position seven to zero: 11011011.
  13. The output is 219 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise XOR operation.

Final answer: 11011011

Boolean logic · Problem 0042

Calculate 00100110 OR 00011000.

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

Reveal detailed solution →
  1. A is the eight-bit string 00100110.
  2. B is the eight-bit string 00011000.
  3. The operation is OR, applied separately to each matching bit position.
  4. Position 7 (weight 128): OR(0, 0) = 0.
  5. Position 6 (weight 64): OR(0, 0) = 0.
  6. Position 5 (weight 32): OR(1, 0) = 1.
  7. Position 4 (weight 16): OR(0, 1) = 1.
  8. Position 3 (weight 8): OR(0, 1) = 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: 00111110.
  13. The output is 62 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise OR operation.

Final answer: 00111110

Boolean logic · Problem 0043

Calculate 00100111 AND 00000111.

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

Reveal detailed solution →
  1. A is the eight-bit string 00100111.
  2. B is the eight-bit string 00000111.
  3. The operation is AND, applied separately to each matching bit position.
  4. Position 7 (weight 128): AND(0, 0) = 0.
  5. Position 6 (weight 64): AND(0, 0) = 0.
  6. Position 5 (weight 32): AND(1, 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(1, 1) = 1.
  10. Position 1 (weight 2): AND(1, 1) = 1.
  11. Position 0 (weight 1): AND(1, 1) = 1.
  12. Concatenate the output bits from position seven to zero: 00000111.
  13. The output is 7 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise AND operation.

Final answer: 00000111

Boolean logic · Problem 0044

Calculate 00100111 AND 00001110.

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

Reveal detailed solution →
  1. A is the eight-bit string 00100111.
  2. B is the eight-bit string 00001110.
  3. The operation is AND, applied separately to each matching bit position.
  4. Position 7 (weight 128): AND(0, 0) = 0.
  5. Position 6 (weight 64): AND(0, 0) = 0.
  6. Position 5 (weight 32): AND(1, 0) = 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(1, 1) = 1.
  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: 00000110.
  13. The output is 6 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise AND operation.

Final answer: 00000110

Boolean logic · Problem 0045

Calculate 00100111 XOR 00100100.

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

Reveal detailed solution →
  1. A is the eight-bit string 00100111.
  2. B is the eight-bit string 00100100.
  3. The operation is XOR, applied separately to each matching bit position.
  4. Position 7 (weight 128): XOR(0, 0) = 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(0, 0) = 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(1, 0) = 1.
  11. Position 0 (weight 1): XOR(1, 0) = 1.
  12. Concatenate the output bits from position seven to zero: 00000011.
  13. The output is 3 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise XOR operation.

Final answer: 00000011

Boolean logic · Problem 0046

Calculate 00101000 AND 11110000.

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

Reveal detailed solution →
  1. A is the eight-bit string 00101000.
  2. B is the eight-bit string 11110000.
  3. The operation is AND, applied separately to each matching bit position.
  4. Position 7 (weight 128): AND(0, 1) = 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(0, 1) = 0.
  8. Position 3 (weight 8): AND(1, 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, 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 0047

Calculate 00101001 OR 11100010.

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

Reveal detailed solution →
  1. A is the eight-bit string 00101001.
  2. B is the eight-bit string 11100010.
  3. The operation is OR, applied separately to each matching bit position.
  4. Position 7 (weight 128): OR(0, 1) = 1.
  5. Position 6 (weight 64): OR(0, 1) = 1.
  6. Position 5 (weight 32): OR(1, 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(0, 0) = 0.
  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: 11101011.
  13. The output is 235 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise OR operation.

Final answer: 11101011

Boolean logic · Problem 0048

Calculate 00101010 AND 11111110.

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

Reveal detailed solution →
  1. A is the eight-bit string 00101010.
  2. B is the eight-bit string 11111110.
  3. The operation is AND, applied separately to each matching bit position.
  4. Position 7 (weight 128): AND(0, 1) = 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(0, 1) = 0.
  8. Position 3 (weight 8): AND(1, 1) = 1.
  9. Position 2 (weight 4): AND(0, 1) = 0.
  10. Position 1 (weight 2): AND(1, 1) = 1.
  11. Position 0 (weight 1): AND(0, 0) = 0.
  12. Concatenate the output bits from position seven to zero: 00101010.
  13. The output is 42 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise AND operation.

Final answer: 00101010

Boolean logic · Problem 0049

Calculate 00101011 OR 00000110.

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

Reveal detailed solution →
  1. A is the eight-bit string 00101011.
  2. B is the eight-bit string 00000110.
  3. The operation is OR, applied separately to each matching bit position.
  4. Position 7 (weight 128): OR(0, 0) = 0.
  5. Position 6 (weight 64): OR(0, 0) = 0.
  6. Position 5 (weight 32): OR(1, 0) = 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(0, 1) = 1.
  10. Position 1 (weight 2): OR(1, 1) = 1.
  11. Position 0 (weight 1): OR(1, 0) = 1.
  12. Concatenate the output bits from position seven to zero: 00101111.
  13. The output is 47 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise OR operation.

Final answer: 00101111

Boolean logic · Problem 0050

Calculate 00101011 OR 01000110.

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

Reveal detailed solution →
  1. A is the eight-bit string 00101011.
  2. B is the eight-bit string 01000110.
  3. The operation is OR, applied separately to each matching bit position.
  4. Position 7 (weight 128): OR(0, 0) = 0.
  5. Position 6 (weight 64): OR(0, 1) = 1.
  6. Position 5 (weight 32): OR(1, 0) = 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(0, 1) = 1.
  10. Position 1 (weight 2): OR(1, 1) = 1.
  11. Position 0 (weight 1): OR(1, 0) = 1.
  12. Concatenate the output bits from position seven to zero: 01101111.
  13. The output is 111 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise OR operation.

Final answer: 01101111

Boolean logic · Problem 0051

Calculate 00101011 AND 01001011.

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

Reveal detailed solution →
  1. A is the eight-bit string 00101011.
  2. B is the eight-bit string 01001011.
  3. The operation is AND, applied separately to each matching bit position.
  4. Position 7 (weight 128): AND(0, 0) = 0.
  5. Position 6 (weight 64): AND(0, 1) = 0.
  6. Position 5 (weight 32): AND(1, 0) = 0.
  7. Position 4 (weight 16): AND(0, 0) = 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, 1) = 1.
  11. Position 0 (weight 1): AND(1, 1) = 1.
  12. Concatenate the output bits from position seven to zero: 00001011.
  13. The output is 11 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise AND operation.

Final answer: 00001011

Boolean logic · Problem 0052

Calculate 00101011 OR 11100100.

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

Reveal detailed solution →
  1. A is the eight-bit string 00101011.
  2. B is the eight-bit string 11100100.
  3. The operation is OR, applied separately to each matching bit position.
  4. Position 7 (weight 128): OR(0, 1) = 1.
  5. Position 6 (weight 64): OR(0, 1) = 1.
  6. Position 5 (weight 32): OR(1, 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(0, 1) = 1.
  10. Position 1 (weight 2): OR(1, 0) = 1.
  11. Position 0 (weight 1): OR(1, 0) = 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 0053

Calculate 00101100 AND 00000010.

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

Reveal detailed solution →
  1. A is the eight-bit string 00101100.
  2. B is the eight-bit string 00000010.
  3. The operation is AND, applied separately to each matching bit position.
  4. Position 7 (weight 128): AND(0, 0) = 0.
  5. Position 6 (weight 64): AND(0, 0) = 0.
  6. Position 5 (weight 32): AND(1, 0) = 0.
  7. Position 4 (weight 16): AND(0, 0) = 0.
  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: 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 0054

Calculate 00101100 OR 10010111.

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

Reveal detailed solution →
  1. A is the eight-bit string 00101100.
  2. B is the eight-bit string 10010111.
  3. The operation is OR, applied separately to each matching bit position.
  4. Position 7 (weight 128): OR(0, 1) = 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(0, 1) = 1.
  8. Position 3 (weight 8): OR(1, 0) = 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(0, 1) = 1.
  12. Concatenate the output bits from position seven to zero: 10111111.
  13. The output is 191 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise OR operation.

Final answer: 10111111

Boolean logic · Problem 0055

Calculate 00101101 OR 00011100.

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

Reveal detailed solution →
  1. A is the eight-bit string 00101101.
  2. B is the eight-bit string 00011100.
  3. The operation is OR, applied separately to each matching bit position.
  4. Position 7 (weight 128): OR(0, 0) = 0.
  5. Position 6 (weight 64): OR(0, 0) = 0.
  6. Position 5 (weight 32): OR(1, 0) = 1.
  7. Position 4 (weight 16): OR(0, 1) = 1.
  8. Position 3 (weight 8): OR(1, 1) = 1.
  9. Position 2 (weight 4): OR(1, 1) = 1.
  10. Position 1 (weight 2): OR(0, 0) = 0.
  11. Position 0 (weight 1): OR(1, 0) = 1.
  12. Concatenate the output bits from position seven to zero: 00111101.
  13. The output is 61 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise OR operation.

Final answer: 00111101

Boolean logic · Problem 0056

Calculate 00101111 AND 00100100.

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

Reveal detailed solution →
  1. A is the eight-bit string 00101111.
  2. B is the eight-bit string 00100100.
  3. The operation is AND, applied separately to each matching bit position.
  4. Position 7 (weight 128): AND(0, 0) = 0.
  5. Position 6 (weight 64): AND(0, 0) = 0.
  6. Position 5 (weight 32): AND(1, 1) = 1.
  7. Position 4 (weight 16): AND(0, 0) = 0.
  8. Position 3 (weight 8): AND(1, 0) = 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: 00100100.
  13. The output is 36 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise AND operation.

Final answer: 00100100

Boolean logic · Problem 0057

Calculate 00110000 XOR 11010001.

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

Reveal detailed solution →
  1. A is the eight-bit string 00110000.
  2. B is the eight-bit string 11010001.
  3. The operation is XOR, applied separately to each matching bit position.
  4. Position 7 (weight 128): XOR(0, 1) = 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(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: 11100001.
  13. The output is 225 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise XOR operation.

Final answer: 11100001

Boolean logic · Problem 0058

Calculate 00110001 OR 10111101.

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

Reveal detailed solution →
  1. A is the eight-bit string 00110001.
  2. B is the eight-bit string 10111101.
  3. The operation is OR, applied separately to each matching bit position.
  4. Position 7 (weight 128): OR(0, 1) = 1.
  5. Position 6 (weight 64): OR(0, 0) = 0.
  6. Position 5 (weight 32): OR(1, 1) = 1.
  7. Position 4 (weight 16): OR(1, 1) = 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, 0) = 0.
  11. Position 0 (weight 1): OR(1, 1) = 1.
  12. Concatenate the output bits from position seven to zero: 10111101.
  13. The output is 189 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise OR operation.

Final answer: 10111101

Boolean logic · Problem 0059

Calculate 00110010 XOR 01000111.

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

Reveal detailed solution →
  1. A is the eight-bit string 00110010.
  2. B is the eight-bit string 01000111.
  3. The operation is XOR, applied separately to each matching bit position.
  4. Position 7 (weight 128): XOR(0, 0) = 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(0, 1) = 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: 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 0060

Calculate 00110010 OR 11001011.

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

Reveal detailed solution →
  1. A is the eight-bit string 00110010.
  2. B is the eight-bit string 11001011.
  3. The operation is OR, applied separately to each matching bit position.
  4. Position 7 (weight 128): OR(0, 1) = 1.
  5. Position 6 (weight 64): OR(0, 1) = 1.
  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, 1) = 1.
  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, 1) = 1.
  12. Concatenate the output bits from position seven to zero: 11111011.
  13. The output is 251 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise OR operation.

Final answer: 11111011

Boolean logic · Problem 0061

Calculate 00110110 AND 00000110.

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

Reveal detailed solution →
  1. A is the eight-bit string 00110110.
  2. B is the eight-bit string 00000110.
  3. The operation is AND, applied separately to each matching bit position.
  4. Position 7 (weight 128): AND(0, 0) = 0.
  5. Position 6 (weight 64): AND(0, 0) = 0.
  6. Position 5 (weight 32): AND(1, 0) = 0.
  7. Position 4 (weight 16): AND(1, 0) = 0.
  8. Position 3 (weight 8): AND(0, 0) = 0.
  9. Position 2 (weight 4): AND(1, 1) = 1.
  10. Position 1 (weight 2): AND(1, 1) = 1.
  11. Position 0 (weight 1): AND(0, 0) = 0.
  12. Concatenate the output bits from position seven to zero: 00000110.
  13. The output is 6 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise AND operation.

Final answer: 00000110

Boolean logic · Problem 0062

Calculate 00110110 OR 01000011.

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

Reveal detailed solution →
  1. A is the eight-bit string 00110110.
  2. B is the eight-bit string 01000011.
  3. The operation is OR, applied separately to each matching bit position.
  4. Position 7 (weight 128): OR(0, 0) = 0.
  5. Position 6 (weight 64): OR(0, 1) = 1.
  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(1, 0) = 1.
  10. Position 1 (weight 2): OR(1, 1) = 1.
  11. Position 0 (weight 1): OR(0, 1) = 1.
  12. Concatenate the output bits from position seven to zero: 01110111.
  13. The output is 119 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise OR operation.

Final answer: 01110111

Boolean logic · Problem 0063

Calculate 00110110 XOR 01000111.

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

Reveal detailed solution →
  1. A is the eight-bit string 00110110.
  2. B is the eight-bit string 01000111.
  3. The operation is XOR, applied separately to each matching bit position.
  4. Position 7 (weight 128): XOR(0, 0) = 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, 1) = 0.
  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: 01110001.
  13. The output is 113 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise XOR operation.

Final answer: 01110001

Boolean logic · Problem 0064

Calculate 00110111 AND 01010100.

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

Reveal detailed solution →
  1. A is the eight-bit string 00110111.
  2. B is the eight-bit string 01010100.
  3. The operation is AND, applied separately to each matching bit position.
  4. Position 7 (weight 128): AND(0, 0) = 0.
  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(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: 00010100.
  13. The output is 20 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise AND operation.

Final answer: 00010100