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Fully solved problem book

Reading binary

Set 2 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 0033

Read 00100000₂ 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: 00100000.
  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 0 at weight 64 contributes 0.
  6. Column 5: bit 1 at weight 32 contributes 32.
  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 32.
  13. Add just the selected weights: 32.
  14. Answer: 00100000₂ = 32₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 32₁₀

Foundations · Problem 0034

Read 00100001₂ 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: 00100001.
  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 0 at weight 64 contributes 0.
  6. Column 5: bit 1 at weight 32 contributes 32.
  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 32 + 1.
  13. Add just the selected weights: 33.
  14. Answer: 00100001₂ = 33₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 33₁₀

Foundations · Problem 0035

Read 00100010₂ 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: 00100010.
  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 0 at weight 64 contributes 0.
  6. Column 5: bit 1 at weight 32 contributes 32.
  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 32 + 2.
  13. Add just the selected weights: 34.
  14. Answer: 00100010₂ = 34₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 34₁₀

Foundations · Problem 0036

Read 00100011₂ 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: 00100011.
  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 0 at weight 64 contributes 0.
  6. Column 5: bit 1 at weight 32 contributes 32.
  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 32 + 2 + 1.
  13. Add just the selected weights: 35.
  14. Answer: 00100011₂ = 35₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 35₁₀

Foundations · Problem 0037

Read 00100100₂ 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: 00100100.
  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 0 at weight 64 contributes 0.
  6. Column 5: bit 1 at weight 32 contributes 32.
  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 32 + 4.
  13. Add just the selected weights: 36.
  14. Answer: 00100100₂ = 36₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 36₁₀

Foundations · Problem 0038

Read 00100101₂ 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: 00100101.
  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 0 at weight 64 contributes 0.
  6. Column 5: bit 1 at weight 32 contributes 32.
  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 32 + 4 + 1.
  13. Add just the selected weights: 37.
  14. Answer: 00100101₂ = 37₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 37₁₀

Foundations · Problem 0039

Read 00100110₂ 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: 00100110.
  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 0 at weight 64 contributes 0.
  6. Column 5: bit 1 at weight 32 contributes 32.
  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 32 + 4 + 2.
  13. Add just the selected weights: 38.
  14. Answer: 00100110₂ = 38₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 38₁₀

Foundations · Problem 0040

Read 00100111₂ 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: 00100111.
  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 0 at weight 64 contributes 0.
  6. Column 5: bit 1 at weight 32 contributes 32.
  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 32 + 4 + 2 + 1.
  13. Add just the selected weights: 39.
  14. Answer: 00100111₂ = 39₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 39₁₀

Foundations · Problem 0041

Read 00101000₂ 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: 00101000.
  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 0 at weight 64 contributes 0.
  6. Column 5: bit 1 at weight 32 contributes 32.
  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 32 + 8.
  13. Add just the selected weights: 40.
  14. Answer: 00101000₂ = 40₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 40₁₀

Foundations · Problem 0042

Read 00101001₂ 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: 00101001.
  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 0 at weight 64 contributes 0.
  6. Column 5: bit 1 at weight 32 contributes 32.
  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 32 + 8 + 1.
  13. Add just the selected weights: 41.
  14. Answer: 00101001₂ = 41₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 41₁₀

Foundations · Problem 0043

Read 00101010₂ 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: 00101010.
  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 0 at weight 64 contributes 0.
  6. Column 5: bit 1 at weight 32 contributes 32.
  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 32 + 8 + 2.
  13. Add just the selected weights: 42.
  14. Answer: 00101010₂ = 42₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 42₁₀

Foundations · Problem 0044

Read 00101011₂ 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: 00101011.
  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 0 at weight 64 contributes 0.
  6. Column 5: bit 1 at weight 32 contributes 32.
  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 32 + 8 + 2 + 1.
  13. Add just the selected weights: 43.
  14. Answer: 00101011₂ = 43₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 43₁₀

Foundations · Problem 0045

Read 00101100₂ 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: 00101100.
  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 0 at weight 64 contributes 0.
  6. Column 5: bit 1 at weight 32 contributes 32.
  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 32 + 8 + 4.
  13. Add just the selected weights: 44.
  14. Answer: 00101100₂ = 44₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 44₁₀

Foundations · Problem 0046

Read 00101101₂ 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: 00101101.
  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 0 at weight 64 contributes 0.
  6. Column 5: bit 1 at weight 32 contributes 32.
  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 32 + 8 + 4 + 1.
  13. Add just the selected weights: 45.
  14. Answer: 00101101₂ = 45₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 45₁₀

Foundations · Problem 0047

Read 00101110₂ 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: 00101110.
  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 0 at weight 64 contributes 0.
  6. Column 5: bit 1 at weight 32 contributes 32.
  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 32 + 8 + 4 + 2.
  13. Add just the selected weights: 46.
  14. Answer: 00101110₂ = 46₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 46₁₀

Foundations · Problem 0048

Read 00101111₂ 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: 00101111.
  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 0 at weight 64 contributes 0.
  6. Column 5: bit 1 at weight 32 contributes 32.
  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 32 + 8 + 4 + 2 + 1.
  13. Add just the selected weights: 47.
  14. Answer: 00101111₂ = 47₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 47₁₀

Foundations · Problem 0049

Read 00110000₂ 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: 00110000.
  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 0 at weight 64 contributes 0.
  6. Column 5: bit 1 at weight 32 contributes 32.
  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 32 + 16.
  13. Add just the selected weights: 48.
  14. Answer: 00110000₂ = 48₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 48₁₀

Foundations · Problem 0050

Read 00110001₂ 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: 00110001.
  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 0 at weight 64 contributes 0.
  6. Column 5: bit 1 at weight 32 contributes 32.
  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 32 + 16 + 1.
  13. Add just the selected weights: 49.
  14. Answer: 00110001₂ = 49₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 49₁₀

Foundations · Problem 0051

Read 00110010₂ 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: 00110010.
  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 0 at weight 64 contributes 0.
  6. Column 5: bit 1 at weight 32 contributes 32.
  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 32 + 16 + 2.
  13. Add just the selected weights: 50.
  14. Answer: 00110010₂ = 50₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 50₁₀

Foundations · Problem 0052

Read 00110011₂ 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: 00110011.
  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 0 at weight 64 contributes 0.
  6. Column 5: bit 1 at weight 32 contributes 32.
  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 32 + 16 + 2 + 1.
  13. Add just the selected weights: 51.
  14. Answer: 00110011₂ = 51₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 51₁₀

Foundations · Problem 0053

Read 00110100₂ 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: 00110100.
  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 0 at weight 64 contributes 0.
  6. Column 5: bit 1 at weight 32 contributes 32.
  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 32 + 16 + 4.
  13. Add just the selected weights: 52.
  14. Answer: 00110100₂ = 52₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 52₁₀

Foundations · Problem 0054

Read 00110101₂ 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: 00110101.
  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 0 at weight 64 contributes 0.
  6. Column 5: bit 1 at weight 32 contributes 32.
  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 32 + 16 + 4 + 1.
  13. Add just the selected weights: 53.
  14. Answer: 00110101₂ = 53₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 53₁₀

Foundations · Problem 0055

Read 00110110₂ 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: 00110110.
  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 0 at weight 64 contributes 0.
  6. Column 5: bit 1 at weight 32 contributes 32.
  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 32 + 16 + 4 + 2.
  13. Add just the selected weights: 54.
  14. Answer: 00110110₂ = 54₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 54₁₀

Foundations · Problem 0056

Read 00110111₂ 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: 00110111.
  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 0 at weight 64 contributes 0.
  6. Column 5: bit 1 at weight 32 contributes 32.
  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 32 + 16 + 4 + 2 + 1.
  13. Add just the selected weights: 55.
  14. Answer: 00110111₂ = 55₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 55₁₀

Foundations · Problem 0057

Read 00111000₂ 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: 00111000.
  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 0 at weight 64 contributes 0.
  6. Column 5: bit 1 at weight 32 contributes 32.
  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 32 + 16 + 8.
  13. Add just the selected weights: 56.
  14. Answer: 00111000₂ = 56₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 56₁₀

Foundations · Problem 0058

Read 00111001₂ 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: 00111001.
  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 0 at weight 64 contributes 0.
  6. Column 5: bit 1 at weight 32 contributes 32.
  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 32 + 16 + 8 + 1.
  13. Add just the selected weights: 57.
  14. Answer: 00111001₂ = 57₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 57₁₀

Foundations · Problem 0059

Read 00111010₂ 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: 00111010.
  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 0 at weight 64 contributes 0.
  6. Column 5: bit 1 at weight 32 contributes 32.
  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 32 + 16 + 8 + 2.
  13. Add just the selected weights: 58.
  14. Answer: 00111010₂ = 58₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 58₁₀

Foundations · Problem 0060

Read 00111011₂ 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: 00111011.
  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 0 at weight 64 contributes 0.
  6. Column 5: bit 1 at weight 32 contributes 32.
  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 32 + 16 + 8 + 2 + 1.
  13. Add just the selected weights: 59.
  14. Answer: 00111011₂ = 59₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 59₁₀

Foundations · Problem 0061

Read 00111100₂ 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: 00111100.
  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 0 at weight 64 contributes 0.
  6. Column 5: bit 1 at weight 32 contributes 32.
  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 32 + 16 + 8 + 4.
  13. Add just the selected weights: 60.
  14. Answer: 00111100₂ = 60₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 60₁₀

Foundations · Problem 0062

Read 00111101₂ 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: 00111101.
  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 0 at weight 64 contributes 0.
  6. Column 5: bit 1 at weight 32 contributes 32.
  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 32 + 16 + 8 + 4 + 1.
  13. Add just the selected weights: 61.
  14. Answer: 00111101₂ = 61₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 61₁₀

Foundations · Problem 0063

Read 00111110₂ 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: 00111110.
  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 0 at weight 64 contributes 0.
  6. Column 5: bit 1 at weight 32 contributes 32.
  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 32 + 16 + 8 + 4 + 2.
  13. Add just the selected weights: 62.
  14. Answer: 00111110₂ = 62₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 62₁₀

Foundations · Problem 0064

Read 00111111₂ 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: 00111111.
  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 0 at weight 64 contributes 0.
  6. Column 5: bit 1 at weight 32 contributes 32.
  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 32 + 16 + 8 + 4 + 2 + 1.
  13. Add just the selected weights: 63.
  14. Answer: 00111111₂ = 63₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 63₁₀