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Reading binary

Set 1 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 0001

Read 00000000₂ 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: 00000000.
  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 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 none.
  13. Add just the selected weights: 0.
  14. Answer: 00000000₂ = 0₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 0₁₀

Foundations · Problem 0002

Read 00000001₂ 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: 00000001.
  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 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 1.
  13. Add just the selected weights: 1.
  14. Answer: 00000001₂ = 1₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 1₁₀

Foundations · Problem 0003

Read 00000010₂ 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: 00000010.
  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 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 2.
  13. Add just the selected weights: 2.
  14. Answer: 00000010₂ = 2₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 2₁₀

Foundations · Problem 0004

Read 00000011₂ 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: 00000011.
  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 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 2 + 1.
  13. Add just the selected weights: 3.
  14. Answer: 00000011₂ = 3₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 3₁₀

Foundations · Problem 0005

Read 00000100₂ 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: 00000100.
  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 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 4.
  13. Add just the selected weights: 4.
  14. Answer: 00000100₂ = 4₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 4₁₀

Foundations · Problem 0006

Read 00000101₂ 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: 00000101.
  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 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 4 + 1.
  13. Add just the selected weights: 5.
  14. Answer: 00000101₂ = 5₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 5₁₀

Foundations · Problem 0007

Read 00000110₂ 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: 00000110.
  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 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 4 + 2.
  13. Add just the selected weights: 6.
  14. Answer: 00000110₂ = 6₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 6₁₀

Foundations · Problem 0008

Read 00000111₂ 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: 00000111.
  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 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 4 + 2 + 1.
  13. Add just the selected weights: 7.
  14. Answer: 00000111₂ = 7₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 7₁₀

Foundations · Problem 0009

Read 00001000₂ 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: 00001000.
  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 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 8.
  13. Add just the selected weights: 8.
  14. Answer: 00001000₂ = 8₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 8₁₀

Foundations · Problem 0010

Read 00001001₂ 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: 00001001.
  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 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 8 + 1.
  13. Add just the selected weights: 9.
  14. Answer: 00001001₂ = 9₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 9₁₀

Foundations · Problem 0011

Read 00001010₂ 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: 00001010.
  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 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 8 + 2.
  13. Add just the selected weights: 10.
  14. Answer: 00001010₂ = 10₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 10₁₀

Foundations · Problem 0012

Read 00001011₂ 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: 00001011.
  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 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 8 + 2 + 1.
  13. Add just the selected weights: 11.
  14. Answer: 00001011₂ = 11₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 11₁₀

Foundations · Problem 0013

Read 00001100₂ 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: 00001100.
  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 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 8 + 4.
  13. Add just the selected weights: 12.
  14. Answer: 00001100₂ = 12₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 12₁₀

Foundations · Problem 0014

Read 00001101₂ 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: 00001101.
  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 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 8 + 4 + 1.
  13. Add just the selected weights: 13.
  14. Answer: 00001101₂ = 13₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 13₁₀

Foundations · Problem 0015

Read 00001110₂ 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: 00001110.
  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 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 8 + 4 + 2.
  13. Add just the selected weights: 14.
  14. Answer: 00001110₂ = 14₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 14₁₀

Foundations · Problem 0016

Read 00001111₂ 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: 00001111.
  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 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 8 + 4 + 2 + 1.
  13. Add just the selected weights: 15.
  14. Answer: 00001111₂ = 15₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 15₁₀

Foundations · Problem 0017

Read 00010000₂ 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: 00010000.
  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 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 16.
  13. Add just the selected weights: 16.
  14. Answer: 00010000₂ = 16₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 16₁₀

Foundations · Problem 0018

Read 00010001₂ 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: 00010001.
  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 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 16 + 1.
  13. Add just the selected weights: 17.
  14. Answer: 00010001₂ = 17₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 17₁₀

Foundations · Problem 0019

Read 00010010₂ 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: 00010010.
  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 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 16 + 2.
  13. Add just the selected weights: 18.
  14. Answer: 00010010₂ = 18₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 18₁₀

Foundations · Problem 0020

Read 00010011₂ 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: 00010011.
  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 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 16 + 2 + 1.
  13. Add just the selected weights: 19.
  14. Answer: 00010011₂ = 19₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 19₁₀

Foundations · Problem 0021

Read 00010100₂ 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: 00010100.
  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 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 16 + 4.
  13. Add just the selected weights: 20.
  14. Answer: 00010100₂ = 20₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 20₁₀

Foundations · Problem 0022

Read 00010101₂ 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: 00010101.
  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 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 16 + 4 + 1.
  13. Add just the selected weights: 21.
  14. Answer: 00010101₂ = 21₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 21₁₀

Foundations · Problem 0023

Read 00010110₂ 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: 00010110.
  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 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 16 + 4 + 2.
  13. Add just the selected weights: 22.
  14. Answer: 00010110₂ = 22₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 22₁₀

Foundations · Problem 0024

Read 00010111₂ 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: 00010111.
  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 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 16 + 4 + 2 + 1.
  13. Add just the selected weights: 23.
  14. Answer: 00010111₂ = 23₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 23₁₀

Foundations · Problem 0025

Read 00011000₂ 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: 00011000.
  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 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 16 + 8.
  13. Add just the selected weights: 24.
  14. Answer: 00011000₂ = 24₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 24₁₀

Foundations · Problem 0026

Read 00011001₂ 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: 00011001.
  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 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 16 + 8 + 1.
  13. Add just the selected weights: 25.
  14. Answer: 00011001₂ = 25₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 25₁₀

Foundations · Problem 0027

Read 00011010₂ 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: 00011010.
  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 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 16 + 8 + 2.
  13. Add just the selected weights: 26.
  14. Answer: 00011010₂ = 26₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 26₁₀

Foundations · Problem 0028

Read 00011011₂ 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: 00011011.
  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 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 16 + 8 + 2 + 1.
  13. Add just the selected weights: 27.
  14. Answer: 00011011₂ = 27₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 27₁₀

Foundations · Problem 0029

Read 00011100₂ 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: 00011100.
  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 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 16 + 8 + 4.
  13. Add just the selected weights: 28.
  14. Answer: 00011100₂ = 28₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 28₁₀

Foundations · Problem 0030

Read 00011101₂ 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: 00011101.
  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 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 16 + 8 + 4 + 1.
  13. Add just the selected weights: 29.
  14. Answer: 00011101₂ = 29₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 29₁₀

Foundations · Problem 0031

Read 00011110₂ 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: 00011110.
  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 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 16 + 8 + 4 + 2.
  13. Add just the selected weights: 30.
  14. Answer: 00011110₂ = 30₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 30₁₀

Foundations · Problem 0032

Read 00011111₂ 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: 00011111.
  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 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 16 + 8 + 4 + 2 + 1.
  13. Add just the selected weights: 31.
  14. Answer: 00011111₂ = 31₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 31₁₀