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Reading binary

Set 3 of 10 · 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.

Foundations · Problem 0065

Read 01000000₂ as an unsigned decimal integer.

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

Reveal detailed solution →
  1. First record that this is an unsigned 8-bit pattern: 01000000.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 8-bit pattern has weight 2^7 = 128.
  4. Column 7: bit 0 at weight 128 contributes 0.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 0 at weight 32 contributes 0.
  7. Column 4: bit 0 at weight 16 contributes 0.
  8. Column 3: bit 0 at weight 8 contributes 0.
  9. Column 2: bit 0 at weight 4 contributes 0.
  10. Column 1: bit 0 at weight 2 contributes 0.
  11. Column 0: bit 0 at weight 1 contributes 0.
  12. The one-bit weights are 64.
  13. Add just the selected weights: 64.
  14. Answer: 01000000₂ = 64₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 64₁₀

Foundations · Problem 0066

Read 01000001₂ as an unsigned decimal integer.

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

Reveal detailed solution →
  1. First record that this is an unsigned 8-bit pattern: 01000001.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 8-bit pattern has weight 2^7 = 128.
  4. Column 7: bit 0 at weight 128 contributes 0.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 0 at weight 32 contributes 0.
  7. Column 4: bit 0 at weight 16 contributes 0.
  8. Column 3: bit 0 at weight 8 contributes 0.
  9. Column 2: bit 0 at weight 4 contributes 0.
  10. Column 1: bit 0 at weight 2 contributes 0.
  11. Column 0: bit 1 at weight 1 contributes 1.
  12. The one-bit weights are 64 + 1.
  13. Add just the selected weights: 65.
  14. Answer: 01000001₂ = 65₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 65₁₀

Foundations · Problem 0067

Read 01000010₂ as an unsigned decimal integer.

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

Reveal detailed solution →
  1. First record that this is an unsigned 8-bit pattern: 01000010.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 8-bit pattern has weight 2^7 = 128.
  4. Column 7: bit 0 at weight 128 contributes 0.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 0 at weight 32 contributes 0.
  7. Column 4: bit 0 at weight 16 contributes 0.
  8. Column 3: bit 0 at weight 8 contributes 0.
  9. Column 2: bit 0 at weight 4 contributes 0.
  10. Column 1: bit 1 at weight 2 contributes 2.
  11. Column 0: bit 0 at weight 1 contributes 0.
  12. The one-bit weights are 64 + 2.
  13. Add just the selected weights: 66.
  14. Answer: 01000010₂ = 66₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 66₁₀

Foundations · Problem 0068

Read 01000011₂ as an unsigned decimal integer.

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

Reveal detailed solution →
  1. First record that this is an unsigned 8-bit pattern: 01000011.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 8-bit pattern has weight 2^7 = 128.
  4. Column 7: bit 0 at weight 128 contributes 0.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 0 at weight 32 contributes 0.
  7. Column 4: bit 0 at weight 16 contributes 0.
  8. Column 3: bit 0 at weight 8 contributes 0.
  9. Column 2: bit 0 at weight 4 contributes 0.
  10. Column 1: bit 1 at weight 2 contributes 2.
  11. Column 0: bit 1 at weight 1 contributes 1.
  12. The one-bit weights are 64 + 2 + 1.
  13. Add just the selected weights: 67.
  14. Answer: 01000011₂ = 67₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 67₁₀

Foundations · Problem 0069

Read 01000100₂ as an unsigned decimal integer.

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

Reveal detailed solution →
  1. First record that this is an unsigned 8-bit pattern: 01000100.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 8-bit pattern has weight 2^7 = 128.
  4. Column 7: bit 0 at weight 128 contributes 0.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 0 at weight 32 contributes 0.
  7. Column 4: bit 0 at weight 16 contributes 0.
  8. Column 3: bit 0 at weight 8 contributes 0.
  9. Column 2: bit 1 at weight 4 contributes 4.
  10. Column 1: bit 0 at weight 2 contributes 0.
  11. Column 0: bit 0 at weight 1 contributes 0.
  12. The one-bit weights are 64 + 4.
  13. Add just the selected weights: 68.
  14. Answer: 01000100₂ = 68₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 68₁₀

Foundations · Problem 0070

Read 01000101₂ as an unsigned decimal integer.

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

Reveal detailed solution →
  1. First record that this is an unsigned 8-bit pattern: 01000101.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 8-bit pattern has weight 2^7 = 128.
  4. Column 7: bit 0 at weight 128 contributes 0.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 0 at weight 32 contributes 0.
  7. Column 4: bit 0 at weight 16 contributes 0.
  8. Column 3: bit 0 at weight 8 contributes 0.
  9. Column 2: bit 1 at weight 4 contributes 4.
  10. Column 1: bit 0 at weight 2 contributes 0.
  11. Column 0: bit 1 at weight 1 contributes 1.
  12. The one-bit weights are 64 + 4 + 1.
  13. Add just the selected weights: 69.
  14. Answer: 01000101₂ = 69₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 69₁₀

Foundations · Problem 0071

Read 01000110₂ as an unsigned decimal integer.

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

Reveal detailed solution →
  1. First record that this is an unsigned 8-bit pattern: 01000110.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 8-bit pattern has weight 2^7 = 128.
  4. Column 7: bit 0 at weight 128 contributes 0.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 0 at weight 32 contributes 0.
  7. Column 4: bit 0 at weight 16 contributes 0.
  8. Column 3: bit 0 at weight 8 contributes 0.
  9. Column 2: bit 1 at weight 4 contributes 4.
  10. Column 1: bit 1 at weight 2 contributes 2.
  11. Column 0: bit 0 at weight 1 contributes 0.
  12. The one-bit weights are 64 + 4 + 2.
  13. Add just the selected weights: 70.
  14. Answer: 01000110₂ = 70₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 70₁₀

Foundations · Problem 0072

Read 01000111₂ as an unsigned decimal integer.

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

Reveal detailed solution →
  1. First record that this is an unsigned 8-bit pattern: 01000111.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 8-bit pattern has weight 2^7 = 128.
  4. Column 7: bit 0 at weight 128 contributes 0.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 0 at weight 32 contributes 0.
  7. Column 4: bit 0 at weight 16 contributes 0.
  8. Column 3: bit 0 at weight 8 contributes 0.
  9. Column 2: bit 1 at weight 4 contributes 4.
  10. Column 1: bit 1 at weight 2 contributes 2.
  11. Column 0: bit 1 at weight 1 contributes 1.
  12. The one-bit weights are 64 + 4 + 2 + 1.
  13. Add just the selected weights: 71.
  14. Answer: 01000111₂ = 71₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 71₁₀

Foundations · Problem 0073

Read 01001000₂ as an unsigned decimal integer.

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

Reveal detailed solution →
  1. First record that this is an unsigned 8-bit pattern: 01001000.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 8-bit pattern has weight 2^7 = 128.
  4. Column 7: bit 0 at weight 128 contributes 0.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 0 at weight 32 contributes 0.
  7. Column 4: bit 0 at weight 16 contributes 0.
  8. Column 3: bit 1 at weight 8 contributes 8.
  9. Column 2: bit 0 at weight 4 contributes 0.
  10. Column 1: bit 0 at weight 2 contributes 0.
  11. Column 0: bit 0 at weight 1 contributes 0.
  12. The one-bit weights are 64 + 8.
  13. Add just the selected weights: 72.
  14. Answer: 01001000₂ = 72₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 72₁₀

Foundations · Problem 0074

Read 01001001₂ as an unsigned decimal integer.

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

Reveal detailed solution →
  1. First record that this is an unsigned 8-bit pattern: 01001001.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 8-bit pattern has weight 2^7 = 128.
  4. Column 7: bit 0 at weight 128 contributes 0.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 0 at weight 32 contributes 0.
  7. Column 4: bit 0 at weight 16 contributes 0.
  8. Column 3: bit 1 at weight 8 contributes 8.
  9. Column 2: bit 0 at weight 4 contributes 0.
  10. Column 1: bit 0 at weight 2 contributes 0.
  11. Column 0: bit 1 at weight 1 contributes 1.
  12. The one-bit weights are 64 + 8 + 1.
  13. Add just the selected weights: 73.
  14. Answer: 01001001₂ = 73₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 73₁₀

Foundations · Problem 0075

Read 01001010₂ as an unsigned decimal integer.

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

Reveal detailed solution →
  1. First record that this is an unsigned 8-bit pattern: 01001010.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 8-bit pattern has weight 2^7 = 128.
  4. Column 7: bit 0 at weight 128 contributes 0.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 0 at weight 32 contributes 0.
  7. Column 4: bit 0 at weight 16 contributes 0.
  8. Column 3: bit 1 at weight 8 contributes 8.
  9. Column 2: bit 0 at weight 4 contributes 0.
  10. Column 1: bit 1 at weight 2 contributes 2.
  11. Column 0: bit 0 at weight 1 contributes 0.
  12. The one-bit weights are 64 + 8 + 2.
  13. Add just the selected weights: 74.
  14. Answer: 01001010₂ = 74₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 74₁₀

Foundations · Problem 0076

Read 01001011₂ as an unsigned decimal integer.

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

Reveal detailed solution →
  1. First record that this is an unsigned 8-bit pattern: 01001011.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 8-bit pattern has weight 2^7 = 128.
  4. Column 7: bit 0 at weight 128 contributes 0.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 0 at weight 32 contributes 0.
  7. Column 4: bit 0 at weight 16 contributes 0.
  8. Column 3: bit 1 at weight 8 contributes 8.
  9. Column 2: bit 0 at weight 4 contributes 0.
  10. Column 1: bit 1 at weight 2 contributes 2.
  11. Column 0: bit 1 at weight 1 contributes 1.
  12. The one-bit weights are 64 + 8 + 2 + 1.
  13. Add just the selected weights: 75.
  14. Answer: 01001011₂ = 75₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 75₁₀

Foundations · Problem 0077

Read 01001100₂ as an unsigned decimal integer.

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

Reveal detailed solution →
  1. First record that this is an unsigned 8-bit pattern: 01001100.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 8-bit pattern has weight 2^7 = 128.
  4. Column 7: bit 0 at weight 128 contributes 0.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 0 at weight 32 contributes 0.
  7. Column 4: bit 0 at weight 16 contributes 0.
  8. Column 3: bit 1 at weight 8 contributes 8.
  9. Column 2: bit 1 at weight 4 contributes 4.
  10. Column 1: bit 0 at weight 2 contributes 0.
  11. Column 0: bit 0 at weight 1 contributes 0.
  12. The one-bit weights are 64 + 8 + 4.
  13. Add just the selected weights: 76.
  14. Answer: 01001100₂ = 76₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 76₁₀

Foundations · Problem 0078

Read 01001101₂ as an unsigned decimal integer.

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

Reveal detailed solution →
  1. First record that this is an unsigned 8-bit pattern: 01001101.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 8-bit pattern has weight 2^7 = 128.
  4. Column 7: bit 0 at weight 128 contributes 0.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 0 at weight 32 contributes 0.
  7. Column 4: bit 0 at weight 16 contributes 0.
  8. Column 3: bit 1 at weight 8 contributes 8.
  9. Column 2: bit 1 at weight 4 contributes 4.
  10. Column 1: bit 0 at weight 2 contributes 0.
  11. Column 0: bit 1 at weight 1 contributes 1.
  12. The one-bit weights are 64 + 8 + 4 + 1.
  13. Add just the selected weights: 77.
  14. Answer: 01001101₂ = 77₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 77₁₀

Foundations · Problem 0079

Read 01001110₂ as an unsigned decimal integer.

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

Reveal detailed solution →
  1. First record that this is an unsigned 8-bit pattern: 01001110.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 8-bit pattern has weight 2^7 = 128.
  4. Column 7: bit 0 at weight 128 contributes 0.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 0 at weight 32 contributes 0.
  7. Column 4: bit 0 at weight 16 contributes 0.
  8. Column 3: bit 1 at weight 8 contributes 8.
  9. Column 2: bit 1 at weight 4 contributes 4.
  10. Column 1: bit 1 at weight 2 contributes 2.
  11. Column 0: bit 0 at weight 1 contributes 0.
  12. The one-bit weights are 64 + 8 + 4 + 2.
  13. Add just the selected weights: 78.
  14. Answer: 01001110₂ = 78₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 78₁₀

Foundations · Problem 0080

Read 01001111₂ as an unsigned decimal integer.

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

Reveal detailed solution →
  1. First record that this is an unsigned 8-bit pattern: 01001111.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 8-bit pattern has weight 2^7 = 128.
  4. Column 7: bit 0 at weight 128 contributes 0.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 0 at weight 32 contributes 0.
  7. Column 4: bit 0 at weight 16 contributes 0.
  8. Column 3: bit 1 at weight 8 contributes 8.
  9. Column 2: bit 1 at weight 4 contributes 4.
  10. Column 1: bit 1 at weight 2 contributes 2.
  11. Column 0: bit 1 at weight 1 contributes 1.
  12. The one-bit weights are 64 + 8 + 4 + 2 + 1.
  13. Add just the selected weights: 79.
  14. Answer: 01001111₂ = 79₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 79₁₀

Foundations · Problem 0081

Read 01010000₂ as an unsigned decimal integer.

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

Reveal detailed solution →
  1. First record that this is an unsigned 8-bit pattern: 01010000.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 8-bit pattern has weight 2^7 = 128.
  4. Column 7: bit 0 at weight 128 contributes 0.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 0 at weight 32 contributes 0.
  7. Column 4: bit 1 at weight 16 contributes 16.
  8. Column 3: bit 0 at weight 8 contributes 0.
  9. Column 2: bit 0 at weight 4 contributes 0.
  10. Column 1: bit 0 at weight 2 contributes 0.
  11. Column 0: bit 0 at weight 1 contributes 0.
  12. The one-bit weights are 64 + 16.
  13. Add just the selected weights: 80.
  14. Answer: 01010000₂ = 80₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 80₁₀

Foundations · Problem 0082

Read 01010001₂ as an unsigned decimal integer.

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

Reveal detailed solution →
  1. First record that this is an unsigned 8-bit pattern: 01010001.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 8-bit pattern has weight 2^7 = 128.
  4. Column 7: bit 0 at weight 128 contributes 0.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 0 at weight 32 contributes 0.
  7. Column 4: bit 1 at weight 16 contributes 16.
  8. Column 3: bit 0 at weight 8 contributes 0.
  9. Column 2: bit 0 at weight 4 contributes 0.
  10. Column 1: bit 0 at weight 2 contributes 0.
  11. Column 0: bit 1 at weight 1 contributes 1.
  12. The one-bit weights are 64 + 16 + 1.
  13. Add just the selected weights: 81.
  14. Answer: 01010001₂ = 81₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 81₁₀

Foundations · Problem 0083

Read 01010010₂ as an unsigned decimal integer.

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

Reveal detailed solution →
  1. First record that this is an unsigned 8-bit pattern: 01010010.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 8-bit pattern has weight 2^7 = 128.
  4. Column 7: bit 0 at weight 128 contributes 0.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 0 at weight 32 contributes 0.
  7. Column 4: bit 1 at weight 16 contributes 16.
  8. Column 3: bit 0 at weight 8 contributes 0.
  9. Column 2: bit 0 at weight 4 contributes 0.
  10. Column 1: bit 1 at weight 2 contributes 2.
  11. Column 0: bit 0 at weight 1 contributes 0.
  12. The one-bit weights are 64 + 16 + 2.
  13. Add just the selected weights: 82.
  14. Answer: 01010010₂ = 82₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 82₁₀

Foundations · Problem 0084

Read 01010011₂ as an unsigned decimal integer.

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

Reveal detailed solution →
  1. First record that this is an unsigned 8-bit pattern: 01010011.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 8-bit pattern has weight 2^7 = 128.
  4. Column 7: bit 0 at weight 128 contributes 0.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 0 at weight 32 contributes 0.
  7. Column 4: bit 1 at weight 16 contributes 16.
  8. Column 3: bit 0 at weight 8 contributes 0.
  9. Column 2: bit 0 at weight 4 contributes 0.
  10. Column 1: bit 1 at weight 2 contributes 2.
  11. Column 0: bit 1 at weight 1 contributes 1.
  12. The one-bit weights are 64 + 16 + 2 + 1.
  13. Add just the selected weights: 83.
  14. Answer: 01010011₂ = 83₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 83₁₀

Foundations · Problem 0085

Read 01010100₂ as an unsigned decimal integer.

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

Reveal detailed solution →
  1. First record that this is an unsigned 8-bit pattern: 01010100.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 8-bit pattern has weight 2^7 = 128.
  4. Column 7: bit 0 at weight 128 contributes 0.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 0 at weight 32 contributes 0.
  7. Column 4: bit 1 at weight 16 contributes 16.
  8. Column 3: bit 0 at weight 8 contributes 0.
  9. Column 2: bit 1 at weight 4 contributes 4.
  10. Column 1: bit 0 at weight 2 contributes 0.
  11. Column 0: bit 0 at weight 1 contributes 0.
  12. The one-bit weights are 64 + 16 + 4.
  13. Add just the selected weights: 84.
  14. Answer: 01010100₂ = 84₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 84₁₀

Foundations · Problem 0086

Read 01010101₂ as an unsigned decimal integer.

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

Reveal detailed solution →
  1. First record that this is an unsigned 8-bit pattern: 01010101.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 8-bit pattern has weight 2^7 = 128.
  4. Column 7: bit 0 at weight 128 contributes 0.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 0 at weight 32 contributes 0.
  7. Column 4: bit 1 at weight 16 contributes 16.
  8. Column 3: bit 0 at weight 8 contributes 0.
  9. Column 2: bit 1 at weight 4 contributes 4.
  10. Column 1: bit 0 at weight 2 contributes 0.
  11. Column 0: bit 1 at weight 1 contributes 1.
  12. The one-bit weights are 64 + 16 + 4 + 1.
  13. Add just the selected weights: 85.
  14. Answer: 01010101₂ = 85₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 85₁₀

Foundations · Problem 0087

Read 01010110₂ as an unsigned decimal integer.

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

Reveal detailed solution →
  1. First record that this is an unsigned 8-bit pattern: 01010110.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 8-bit pattern has weight 2^7 = 128.
  4. Column 7: bit 0 at weight 128 contributes 0.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 0 at weight 32 contributes 0.
  7. Column 4: bit 1 at weight 16 contributes 16.
  8. Column 3: bit 0 at weight 8 contributes 0.
  9. Column 2: bit 1 at weight 4 contributes 4.
  10. Column 1: bit 1 at weight 2 contributes 2.
  11. Column 0: bit 0 at weight 1 contributes 0.
  12. The one-bit weights are 64 + 16 + 4 + 2.
  13. Add just the selected weights: 86.
  14. Answer: 01010110₂ = 86₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 86₁₀

Foundations · Problem 0088

Read 01010111₂ as an unsigned decimal integer.

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

Reveal detailed solution →
  1. First record that this is an unsigned 8-bit pattern: 01010111.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 8-bit pattern has weight 2^7 = 128.
  4. Column 7: bit 0 at weight 128 contributes 0.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 0 at weight 32 contributes 0.
  7. Column 4: bit 1 at weight 16 contributes 16.
  8. Column 3: bit 0 at weight 8 contributes 0.
  9. Column 2: bit 1 at weight 4 contributes 4.
  10. Column 1: bit 1 at weight 2 contributes 2.
  11. Column 0: bit 1 at weight 1 contributes 1.
  12. The one-bit weights are 64 + 16 + 4 + 2 + 1.
  13. Add just the selected weights: 87.
  14. Answer: 01010111₂ = 87₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 87₁₀

Foundations · Problem 0089

Read 01011000₂ as an unsigned decimal integer.

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

Reveal detailed solution →
  1. First record that this is an unsigned 8-bit pattern: 01011000.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 8-bit pattern has weight 2^7 = 128.
  4. Column 7: bit 0 at weight 128 contributes 0.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 0 at weight 32 contributes 0.
  7. Column 4: bit 1 at weight 16 contributes 16.
  8. Column 3: bit 1 at weight 8 contributes 8.
  9. Column 2: bit 0 at weight 4 contributes 0.
  10. Column 1: bit 0 at weight 2 contributes 0.
  11. Column 0: bit 0 at weight 1 contributes 0.
  12. The one-bit weights are 64 + 16 + 8.
  13. Add just the selected weights: 88.
  14. Answer: 01011000₂ = 88₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 88₁₀

Foundations · Problem 0090

Read 01011001₂ as an unsigned decimal integer.

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

Reveal detailed solution →
  1. First record that this is an unsigned 8-bit pattern: 01011001.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 8-bit pattern has weight 2^7 = 128.
  4. Column 7: bit 0 at weight 128 contributes 0.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 0 at weight 32 contributes 0.
  7. Column 4: bit 1 at weight 16 contributes 16.
  8. Column 3: bit 1 at weight 8 contributes 8.
  9. Column 2: bit 0 at weight 4 contributes 0.
  10. Column 1: bit 0 at weight 2 contributes 0.
  11. Column 0: bit 1 at weight 1 contributes 1.
  12. The one-bit weights are 64 + 16 + 8 + 1.
  13. Add just the selected weights: 89.
  14. Answer: 01011001₂ = 89₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 89₁₀

Foundations · Problem 0091

Read 01011010₂ as an unsigned decimal integer.

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

Reveal detailed solution →
  1. First record that this is an unsigned 8-bit pattern: 01011010.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 8-bit pattern has weight 2^7 = 128.
  4. Column 7: bit 0 at weight 128 contributes 0.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 0 at weight 32 contributes 0.
  7. Column 4: bit 1 at weight 16 contributes 16.
  8. Column 3: bit 1 at weight 8 contributes 8.
  9. Column 2: bit 0 at weight 4 contributes 0.
  10. Column 1: bit 1 at weight 2 contributes 2.
  11. Column 0: bit 0 at weight 1 contributes 0.
  12. The one-bit weights are 64 + 16 + 8 + 2.
  13. Add just the selected weights: 90.
  14. Answer: 01011010₂ = 90₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 90₁₀

Foundations · Problem 0092

Read 01011011₂ as an unsigned decimal integer.

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

Reveal detailed solution →
  1. First record that this is an unsigned 8-bit pattern: 01011011.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 8-bit pattern has weight 2^7 = 128.
  4. Column 7: bit 0 at weight 128 contributes 0.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 0 at weight 32 contributes 0.
  7. Column 4: bit 1 at weight 16 contributes 16.
  8. Column 3: bit 1 at weight 8 contributes 8.
  9. Column 2: bit 0 at weight 4 contributes 0.
  10. Column 1: bit 1 at weight 2 contributes 2.
  11. Column 0: bit 1 at weight 1 contributes 1.
  12. The one-bit weights are 64 + 16 + 8 + 2 + 1.
  13. Add just the selected weights: 91.
  14. Answer: 01011011₂ = 91₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 91₁₀

Foundations · Problem 0093

Read 01011100₂ as an unsigned decimal integer.

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

Reveal detailed solution →
  1. First record that this is an unsigned 8-bit pattern: 01011100.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 8-bit pattern has weight 2^7 = 128.
  4. Column 7: bit 0 at weight 128 contributes 0.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 0 at weight 32 contributes 0.
  7. Column 4: bit 1 at weight 16 contributes 16.
  8. Column 3: bit 1 at weight 8 contributes 8.
  9. Column 2: bit 1 at weight 4 contributes 4.
  10. Column 1: bit 0 at weight 2 contributes 0.
  11. Column 0: bit 0 at weight 1 contributes 0.
  12. The one-bit weights are 64 + 16 + 8 + 4.
  13. Add just the selected weights: 92.
  14. Answer: 01011100₂ = 92₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 92₁₀

Foundations · Problem 0094

Read 01011101₂ as an unsigned decimal integer.

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

Reveal detailed solution →
  1. First record that this is an unsigned 8-bit pattern: 01011101.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 8-bit pattern has weight 2^7 = 128.
  4. Column 7: bit 0 at weight 128 contributes 0.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 0 at weight 32 contributes 0.
  7. Column 4: bit 1 at weight 16 contributes 16.
  8. Column 3: bit 1 at weight 8 contributes 8.
  9. Column 2: bit 1 at weight 4 contributes 4.
  10. Column 1: bit 0 at weight 2 contributes 0.
  11. Column 0: bit 1 at weight 1 contributes 1.
  12. The one-bit weights are 64 + 16 + 8 + 4 + 1.
  13. Add just the selected weights: 93.
  14. Answer: 01011101₂ = 93₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 93₁₀

Foundations · Problem 0095

Read 01011110₂ as an unsigned decimal integer.

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

Reveal detailed solution →
  1. First record that this is an unsigned 8-bit pattern: 01011110.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 8-bit pattern has weight 2^7 = 128.
  4. Column 7: bit 0 at weight 128 contributes 0.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 0 at weight 32 contributes 0.
  7. Column 4: bit 1 at weight 16 contributes 16.
  8. Column 3: bit 1 at weight 8 contributes 8.
  9. Column 2: bit 1 at weight 4 contributes 4.
  10. Column 1: bit 1 at weight 2 contributes 2.
  11. Column 0: bit 0 at weight 1 contributes 0.
  12. The one-bit weights are 64 + 16 + 8 + 4 + 2.
  13. Add just the selected weights: 94.
  14. Answer: 01011110₂ = 94₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 94₁₀

Foundations · Problem 0096

Read 01011111₂ as an unsigned decimal integer.

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

Reveal detailed solution →
  1. First record that this is an unsigned 8-bit pattern: 01011111.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 8-bit pattern has weight 2^7 = 128.
  4. Column 7: bit 0 at weight 128 contributes 0.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 0 at weight 32 contributes 0.
  7. Column 4: bit 1 at weight 16 contributes 16.
  8. Column 3: bit 1 at weight 8 contributes 8.
  9. Column 2: bit 1 at weight 4 contributes 4.
  10. Column 1: bit 1 at weight 2 contributes 2.
  11. Column 0: bit 1 at weight 1 contributes 1.
  12. The one-bit weights are 64 + 16 + 8 + 4 + 2 + 1.
  13. Add just the selected weights: 95.
  14. Answer: 01011111₂ = 95₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 95₁₀