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Practice library / Bitwise logic

Fully solved problem book

Bitwise logic

Set 1 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 0001

Calculate 00000001 XOR 01000001.

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

Reveal detailed solution →
  1. A is the eight-bit string 00000001.
  2. B is the eight-bit string 01000001.
  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(0, 0) = 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(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

Boolean logic · Problem 0002

Calculate 00000010 XOR 01101100.

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

Reveal detailed solution →
  1. A is the eight-bit string 00000010.
  2. B is the eight-bit string 01101100.
  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(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(0, 1) = 1.
  10. Position 1 (weight 2): XOR(1, 0) = 1.
  11. Position 0 (weight 1): XOR(0, 0) = 0.
  12. Concatenate the output bits from position seven to zero: 01101110.
  13. The output is 110 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise XOR operation.

Final answer: 01101110

Boolean logic · Problem 0003

Calculate 00000100 AND 00110111.

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

Reveal detailed solution →
  1. A is the eight-bit string 00000100.
  2. B is the eight-bit string 00110111.
  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(0, 1) = 0.
  7. Position 4 (weight 16): AND(0, 1) = 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(0, 1) = 0.
  11. Position 0 (weight 1): AND(0, 1) = 0.
  12. Concatenate the output bits from position seven to zero: 00000100.
  13. The output is 4 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise AND operation.

Final answer: 00000100

Boolean logic · Problem 0004

Calculate 00000100 XOR 01111011.

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

Reveal detailed solution →
  1. A is the eight-bit string 00000100.
  2. B is the eight-bit string 01111011.
  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(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, 0) = 1.
  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: 01111111.
  13. The output is 127 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise XOR operation.

Final answer: 01111111

Boolean logic · Problem 0005

Calculate 00000101 OR 00111011.

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

Reveal detailed solution →
  1. A is the eight-bit string 00000101.
  2. B is the eight-bit string 00111011.
  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, 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(1, 0) = 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: 00111111.
  13. The output is 63 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise OR operation.

Final answer: 00111111

Boolean logic · Problem 0006

Calculate 00000110 XOR 11100100.

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

Reveal detailed solution →
  1. A is the eight-bit string 00000110.
  2. B is the eight-bit string 11100100.
  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(0, 1) = 1.
  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(0, 0) = 0.
  12. Concatenate the output bits from position seven to zero: 11100010.
  13. The output is 226 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise XOR operation.

Final answer: 11100010

Boolean logic · Problem 0007

Calculate 00001000 AND 00110000.

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

Reveal detailed solution →
  1. A is the eight-bit string 00001000.
  2. B is the eight-bit string 00110000.
  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(0, 1) = 0.
  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: 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 0008

Calculate 00001000 XOR 01100100.

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

Reveal detailed solution →
  1. A is the eight-bit string 00001000.
  2. B is the eight-bit string 01100100.
  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(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(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: 01101100.
  13. The output is 108 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise XOR operation.

Final answer: 01101100

Boolean logic · Problem 0009

Calculate 00001000 OR 10010100.

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

Reveal detailed solution →
  1. A is the eight-bit string 00001000.
  2. B is the eight-bit string 10010100.
  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(0, 0) = 0.
  7. Position 4 (weight 16): OR(0, 1) = 1.
  8. Position 3 (weight 8): OR(1, 0) = 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(0, 0) = 0.
  12. Concatenate the output bits from position seven to zero: 10011100.
  13. The output is 156 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise OR operation.

Final answer: 10011100

Boolean logic · Problem 0010

Calculate 00001011 AND 00010011.

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

Reveal detailed solution →
  1. A is the eight-bit string 00001011.
  2. B is the eight-bit string 00010011.
  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(0, 0) = 0.
  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(1, 1) = 1.
  11. Position 0 (weight 1): AND(1, 1) = 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 AND operation.

Final answer: 00000011

Boolean logic · Problem 0011

Calculate 00001011 XOR 01101101.

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

Reveal detailed solution →
  1. A is the eight-bit string 00001011.
  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(0, 1) = 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(0, 1) = 1.
  10. Position 1 (weight 2): XOR(1, 0) = 1.
  11. Position 0 (weight 1): XOR(1, 1) = 0.
  12. Concatenate the output bits from position seven to zero: 01100110.
  13. The output is 102 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise XOR operation.

Final answer: 01100110

Boolean logic · Problem 0012

Calculate 00001100 AND 01110111.

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

Reveal detailed solution →
  1. A is the eight-bit string 00001100.
  2. B is the eight-bit string 01110111.
  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(0, 1) = 0.
  7. Position 4 (weight 16): AND(0, 1) = 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(0, 1) = 0.
  11. Position 0 (weight 1): AND(0, 1) = 0.
  12. Concatenate the output bits from position seven to zero: 00000100.
  13. The output is 4 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise AND operation.

Final answer: 00000100

Boolean logic · Problem 0013

Calculate 00001100 AND 10110010.

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

Reveal detailed solution →
  1. A is the eight-bit string 00001100.
  2. B is the eight-bit string 10110010.
  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, 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(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 0014

Calculate 00001111 AND 01101110.

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

Reveal detailed solution →
  1. A is the eight-bit string 00001111.
  2. B is the eight-bit string 01101110.
  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(0, 1) = 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(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: 00001110.
  13. The output is 14 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise AND operation.

Final answer: 00001110

Boolean logic · Problem 0015

Calculate 00001111 AND 11010101.

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

Reveal detailed solution →
  1. A is the eight-bit string 00001111.
  2. B is the eight-bit string 11010101.
  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, 0) = 0.
  7. Position 4 (weight 16): AND(0, 1) = 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, 1) = 1.
  12. Concatenate the output bits from position seven to zero: 00000101.
  13. The output is 5 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise AND operation.

Final answer: 00000101

Boolean logic · Problem 0016

Calculate 00010001 XOR 00000001.

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

Reveal detailed solution →
  1. A is the eight-bit string 00010001.
  2. B is the eight-bit string 00000001.
  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(0, 0) = 0.
  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, 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: 00010000.
  13. The output is 16 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise XOR operation.

Final answer: 00010000

Boolean logic · Problem 0017

Calculate 00010100 XOR 00001010.

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

Reveal detailed solution →
  1. A is the eight-bit string 00010100.
  2. B is the eight-bit string 00001010.
  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(0, 0) = 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, 1) = 1.
  11. Position 0 (weight 1): XOR(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 XOR operation.

Final answer: 00011110

Boolean logic · Problem 0018

Calculate 00010100 OR 01011100.

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

Reveal detailed solution →
  1. A is the eight-bit string 00010100.
  2. B is the eight-bit string 01011100.
  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(0, 0) = 0.
  7. Position 4 (weight 16): OR(1, 1) = 1.
  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, 0) = 0.
  11. Position 0 (weight 1): OR(0, 0) = 0.
  12. Concatenate the output bits from position seven to zero: 01011100.
  13. The output is 92 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise OR operation.

Final answer: 01011100

Boolean logic · Problem 0019

Calculate 00010101 AND 11011010.

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

Reveal detailed solution →
  1. A is the eight-bit string 00010101.
  2. B is the eight-bit string 11011010.
  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, 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, 0) = 0.
  10. Position 1 (weight 2): AND(0, 1) = 0.
  11. Position 0 (weight 1): AND(1, 0) = 0.
  12. Concatenate the output bits from position seven to zero: 00010000.
  13. The output is 16 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise AND operation.

Final answer: 00010000

Boolean logic · Problem 0020

Calculate 00010110 AND 10110110.

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

Reveal detailed solution →
  1. A is the eight-bit string 00010110.
  2. B is the eight-bit string 10110110.
  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, 0) = 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(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: 00010110.
  13. The output is 22 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise AND operation.

Final answer: 00010110

Boolean logic · Problem 0021

Calculate 00010111 OR 01101111.

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

Reveal detailed solution →
  1. A is the eight-bit string 00010111.
  2. B is the eight-bit string 01101111.
  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(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(1, 1) = 1.
  10. Position 1 (weight 2): OR(1, 1) = 1.
  11. Position 0 (weight 1): OR(1, 1) = 1.
  12. Concatenate the output bits from position seven to zero: 01111111.
  13. The output is 127 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise OR operation.

Final answer: 01111111

Boolean logic · Problem 0022

Calculate 00010111 XOR 10100101.

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

Reveal detailed solution →
  1. A is the eight-bit string 00010111.
  2. B is the eight-bit string 10100101.
  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, 0) = 0.
  6. Position 5 (weight 32): XOR(0, 1) = 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, 0) = 1.
  11. Position 0 (weight 1): XOR(1, 1) = 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 XOR operation.

Final answer: 10110010

Boolean logic · Problem 0023

Calculate 00010111 AND 10111001.

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

Reveal detailed solution →
  1. A is the eight-bit string 00010111.
  2. B is the eight-bit string 10111001.
  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, 0) = 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(0, 1) = 0.
  9. Position 2 (weight 4): AND(1, 0) = 0.
  10. Position 1 (weight 2): AND(1, 0) = 0.
  11. Position 0 (weight 1): AND(1, 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 AND operation.

Final answer: 00010001

Boolean logic · Problem 0024

Calculate 00010111 AND 11101100.

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

Reveal detailed solution →
  1. A is the eight-bit string 00010111.
  2. B is the eight-bit string 11101100.
  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, 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, 0) = 0.
  11. Position 0 (weight 1): AND(1, 0) = 0.
  12. Concatenate the output bits from position seven to zero: 00000100.
  13. The output is 4 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise AND operation.

Final answer: 00000100

Boolean logic · Problem 0025

Calculate 00011001 AND 11101000.

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

Reveal detailed solution →
  1. A is the eight-bit string 00011001.
  2. B is the eight-bit string 11101000.
  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, 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(0, 0) = 0.
  11. Position 0 (weight 1): AND(1, 0) = 0.
  12. Concatenate the output bits from position seven to zero: 00001000.
  13. The output is 8 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise AND operation.

Final answer: 00001000

Boolean logic · Problem 0026

Calculate 00011001 XOR 11111111.

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

Reveal detailed solution →
  1. A is the eight-bit string 00011001.
  2. B is the eight-bit string 11111111.
  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(0, 1) = 1.
  7. Position 4 (weight 16): XOR(1, 1) = 0.
  8. Position 3 (weight 8): XOR(1, 1) = 0.
  9. Position 2 (weight 4): XOR(0, 1) = 1.
  10. Position 1 (weight 2): XOR(0, 1) = 1.
  11. Position 0 (weight 1): XOR(1, 1) = 0.
  12. Concatenate the output bits from position seven to zero: 11100110.
  13. The output is 230 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise XOR operation.

Final answer: 11100110

Boolean logic · Problem 0027

Calculate 00011010 OR 00110010.

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

Reveal detailed solution →
  1. A is the eight-bit string 00011010.
  2. B is the eight-bit string 00110010.
  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, 1) = 1.
  7. Position 4 (weight 16): OR(1, 1) = 1.
  8. Position 3 (weight 8): OR(1, 0) = 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, 0) = 0.
  12. Concatenate the output bits from position seven to zero: 00111010.
  13. The output is 58 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise OR operation.

Final answer: 00111010

Boolean logic · Problem 0028

Calculate 00011010 AND 00111010.

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

Reveal detailed solution →
  1. A is the eight-bit string 00011010.
  2. B is the eight-bit string 00111010.
  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(0, 1) = 0.
  7. Position 4 (weight 16): AND(1, 1) = 1.
  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(0, 0) = 0.
  12. Concatenate the output bits from position seven to zero: 00011010.
  13. The output is 26 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise AND operation.

Final answer: 00011010

Boolean logic · Problem 0029

Calculate 00011010 XOR 01111100.

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

Reveal detailed solution →
  1. A is the eight-bit string 00011010.
  2. B is the eight-bit string 01111100.
  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(0, 1) = 1.
  7. Position 4 (weight 16): XOR(1, 1) = 0.
  8. Position 3 (weight 8): XOR(1, 1) = 0.
  9. Position 2 (weight 4): XOR(0, 1) = 1.
  10. Position 1 (weight 2): XOR(1, 0) = 1.
  11. Position 0 (weight 1): XOR(0, 0) = 0.
  12. Concatenate the output bits from position seven to zero: 01100110.
  13. The output is 102 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise XOR operation.

Final answer: 01100110

Boolean logic · Problem 0030

Calculate 00011011 XOR 11010100.

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

Reveal detailed solution →
  1. A is the eight-bit string 00011011.
  2. B is the eight-bit string 11010100.
  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(0, 0) = 0.
  7. Position 4 (weight 16): XOR(1, 1) = 0.
  8. Position 3 (weight 8): XOR(1, 0) = 1.
  9. Position 2 (weight 4): XOR(0, 1) = 1.
  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: 11001111.
  13. The output is 207 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise XOR operation.

Final answer: 11001111

Boolean logic · Problem 0031

Calculate 00011101 AND 10110100.

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

Reveal detailed solution →
  1. A is the eight-bit string 00011101.
  2. B is the eight-bit string 10110100.
  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, 0) = 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(0, 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

Boolean logic · Problem 0032

Calculate 00011110 OR 00001011.

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 00001011.
  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, 0) = 1.
  8. Position 3 (weight 8): OR(1, 1) = 1.
  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: 00011111.
  13. The output is 31 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise OR operation.

Final answer: 00011111