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Practice library / Bitwise logic

Fully solved problem book

Bitwise logic

Set 4 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 0097

Calculate 01010110 AND 11101000.

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

Reveal detailed solution →
  1. A is the eight-bit string 01010110.
  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(1, 1) = 1.
  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, 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: 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 0098

Calculate 01010111 OR 00100001.

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

Reveal detailed solution →
  1. A is the eight-bit string 01010111.
  2. B is the eight-bit string 00100001.
  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(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, 0) = 0.
  9. Position 2 (weight 4): OR(1, 0) = 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: 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 0099

Calculate 01011001 XOR 00101100.

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

Reveal detailed solution →
  1. A is the eight-bit string 01011001.
  2. B is the eight-bit string 00101100.
  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(1, 0) = 1.
  6. Position 5 (weight 32): XOR(0, 1) = 1.
  7. Position 4 (weight 16): XOR(1, 0) = 1.
  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, 0) = 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 0100

Calculate 01011001 XOR 01100111.

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

Reveal detailed solution →
  1. A is the eight-bit string 01011001.
  2. B is the eight-bit string 01100111.
  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(1, 1) = 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(1, 0) = 1.
  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: 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 0101

Calculate 01011011 OR 01011100.

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

Reveal detailed solution →
  1. A is the eight-bit string 01011011.
  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(1, 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(1, 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, 0) = 1.
  12. Concatenate the output bits from position seven to zero: 01011111.
  13. The output is 95 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise OR operation.

Final answer: 01011111

Boolean logic · Problem 0102

Calculate 01011011 XOR 01100010.

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

Reveal detailed solution →
  1. A is the eight-bit string 01011011.
  2. B is the eight-bit string 01100010.
  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(1, 1) = 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(1, 0) = 1.
  9. Position 2 (weight 4): XOR(0, 0) = 0.
  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: 00111001.
  13. The output is 57 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise XOR operation.

Final answer: 00111001

Boolean logic · Problem 0103

Calculate 01011011 OR 11010001.

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

Reveal detailed solution →
  1. A is the eight-bit string 01011011.
  2. B is the eight-bit string 11010001.
  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(1, 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(1, 0) = 1.
  9. Position 2 (weight 4): OR(0, 0) = 0.
  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: 11011011.
  13. The output is 219 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise OR operation.

Final answer: 11011011

Boolean logic · Problem 0104

Calculate 01011100 AND 10011100.

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

Reveal detailed solution →
  1. A is the eight-bit string 01011100.
  2. B is the eight-bit string 10011100.
  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(1, 0) = 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(1, 1) = 1.
  9. Position 2 (weight 4): AND(1, 1) = 1.
  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: 00011100.
  13. The output is 28 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise AND operation.

Final answer: 00011100

Boolean logic · Problem 0105

Calculate 01011111 AND 01110100.

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

Reveal detailed solution →
  1. A is the eight-bit string 01011111.
  2. B is the eight-bit string 01110100.
  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(1, 1) = 1.
  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(1, 0) = 0.
  12. Concatenate the output bits from position seven to zero: 01010100.
  13. The output is 84 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise AND operation.

Final answer: 01010100

Boolean logic · Problem 0106

Calculate 01011111 OR 10110010.

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

Reveal detailed solution →
  1. A is the eight-bit string 01011111.
  2. B is the eight-bit string 10110010.
  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(1, 0) = 1.
  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(1, 0) = 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: 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 0107

Calculate 01011111 AND 10110110.

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

Reveal detailed solution →
  1. A is the eight-bit string 01011111.
  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(1, 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(1, 1) = 1.
  11. Position 0 (weight 1): AND(1, 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 0108

Calculate 01100000 XOR 00011111.

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

Reveal detailed solution →
  1. A is the eight-bit string 01100000.
  2. B is the eight-bit string 00011111.
  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(1, 0) = 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, 1) = 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 0109

Calculate 01100000 OR 11010100.

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

Reveal detailed solution →
  1. A is the eight-bit string 01100000.
  2. B is the eight-bit string 11010100.
  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(1, 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, 0) = 0.
  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: 11110100.
  13. The output is 244 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise OR operation.

Final answer: 11110100

Boolean logic · Problem 0110

Calculate 01100011 AND 01111000.

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

Reveal detailed solution →
  1. A is the eight-bit string 01100011.
  2. B is the eight-bit string 01111000.
  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(1, 1) = 1.
  6. Position 5 (weight 32): AND(1, 1) = 1.
  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, 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: 01100000.
  13. The output is 96 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise AND operation.

Final answer: 01100000

Boolean logic · Problem 0111

Calculate 01100011 OR 11111001.

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

Reveal detailed solution →
  1. A is the eight-bit string 01100011.
  2. B is the eight-bit string 11111001.
  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(1, 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, 0) = 0.
  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: 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 0112

Calculate 01100100 AND 00001010.

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

Reveal detailed solution →
  1. A is the eight-bit string 01100100.
  2. B is the eight-bit string 00001010.
  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(1, 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, 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 0113

Calculate 01101000 AND 10000010.

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

Reveal detailed solution →
  1. A is the eight-bit string 01101000.
  2. B is the eight-bit string 10000010.
  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(1, 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(0, 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 0114

Calculate 01101001 AND 01000100.

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

Reveal detailed solution →
  1. A is the eight-bit string 01101001.
  2. B is the eight-bit string 01000100.
  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(1, 1) = 1.
  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(0, 1) = 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: 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 0115

Calculate 01101001 XOR 01010111.

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

Reveal detailed solution →
  1. A is the eight-bit string 01101001.
  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(0, 0) = 0.
  5. Position 6 (weight 64): XOR(1, 1) = 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(1, 0) = 1.
  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: 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 0116

Calculate 01101001 OR 10100010.

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

Reveal detailed solution →
  1. A is the eight-bit string 01101001.
  2. B is the eight-bit string 10100010.
  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(1, 0) = 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 0117

Calculate 01101010 XOR 00010110.

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

Reveal detailed solution →
  1. A is the eight-bit string 01101010.
  2. B is the eight-bit string 00010110.
  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(1, 0) = 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(1, 0) = 1.
  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, 0) = 0.
  12. Concatenate the output bits from position seven to zero: 01111100.
  13. The output is 124 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise XOR operation.

Final answer: 01111100

Boolean logic · Problem 0118

Calculate 01101011 AND 00010000.

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

Reveal detailed solution →
  1. A is the eight-bit string 01101011.
  2. B is the eight-bit string 00010000.
  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(1, 0) = 0.
  6. Position 5 (weight 32): AND(1, 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, 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 0119

Calculate 01101011 OR 10010010.

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

Reveal detailed solution →
  1. A is the eight-bit string 01101011.
  2. B is the eight-bit string 10010010.
  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(1, 0) = 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(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(1, 0) = 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 0120

Calculate 01101100 OR 11100110.

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

Reveal detailed solution →
  1. A is the eight-bit string 01101100.
  2. B is the eight-bit string 11100110.
  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(1, 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(1, 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: 11101110.
  13. The output is 238 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise OR operation.

Final answer: 11101110

Boolean logic · Problem 0121

Calculate 01101100 XOR 11111101.

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

Reveal detailed solution →
  1. A is the eight-bit string 01101100.
  2. B is the eight-bit string 11111101.
  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(1, 1) = 0.
  6. Position 5 (weight 32): XOR(1, 1) = 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, 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: 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 0122

Calculate 01101110 XOR 10110101.

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

Reveal detailed solution →
  1. A is the eight-bit string 01101110.
  2. B is the eight-bit string 10110101.
  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(1, 0) = 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(1, 0) = 1.
  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: 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 0123

Calculate 01101110 OR 11100110.

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

Reveal detailed solution →
  1. A is the eight-bit string 01101110.
  2. B is the eight-bit string 11100110.
  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(1, 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(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: 11101110.
  13. The output is 238 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise OR operation.

Final answer: 11101110

Boolean logic · Problem 0124

Calculate 01101111 OR 00111010.

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

Reveal detailed solution →
  1. A is the eight-bit string 01101111.
  2. B is the eight-bit string 00111010.
  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(1, 0) = 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(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(1, 0) = 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 0125

Calculate 01110000 AND 00011000.

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

Reveal detailed solution →
  1. A is the eight-bit string 01110000.
  2. B is the eight-bit string 00011000.
  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(1, 0) = 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(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: 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 0126

Calculate 01110000 XOR 10101000.

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

Reveal detailed solution →
  1. A is the eight-bit string 01110000.
  2. B is the eight-bit string 10101000.
  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(1, 0) = 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(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: 11011000.
  13. The output is 216 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise XOR operation.

Final answer: 11011000

Boolean logic · Problem 0127

Calculate 01110010 OR 10000101.

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

Reveal detailed solution →
  1. A is the eight-bit string 01110010.
  2. B is the eight-bit string 10000101.
  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(1, 0) = 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(0, 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: 11110111.
  13. The output is 247 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise OR operation.

Final answer: 11110111

Boolean logic · Problem 0128

Calculate 01110010 OR 10100000.

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

Reveal detailed solution →
  1. A is the eight-bit string 01110010.
  2. B is the eight-bit string 10100000.
  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(1, 0) = 1.
  6. Position 5 (weight 32): OR(1, 1) = 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, 0) = 1.
  11. Position 0 (weight 1): OR(0, 0) = 0.
  12. Concatenate the output bits from position seven to zero: 11110010.
  13. The output is 242 when interpreted as unsigned decimal.
  14. No arithmetic carries occur in a bitwise OR operation.

Final answer: 11110010