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Reading binary

Set 10 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 0289

Read 100100000₂ 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 9-bit pattern: 100100000.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 9-bit pattern has weight 2^8 = 256.
  4. Column 8: bit 1 at weight 256 contributes 256.
  5. Column 7: bit 0 at weight 128 contributes 0.
  6. Column 6: bit 0 at weight 64 contributes 0.
  7. Column 5: bit 1 at weight 32 contributes 32.
  8. Column 4: bit 0 at weight 16 contributes 0.
  9. Column 3: bit 0 at weight 8 contributes 0.
  10. Column 2: bit 0 at weight 4 contributes 0.
  11. Column 1: bit 0 at weight 2 contributes 0.
  12. Column 0: bit 0 at weight 1 contributes 0.
  13. The one-bit weights are 256 + 32.
  14. Add just the selected weights: 288.
  15. Answer: 100100000₂ = 288₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 288₁₀

Foundations · Problem 0290

Read 100100001₂ 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 9-bit pattern: 100100001.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 9-bit pattern has weight 2^8 = 256.
  4. Column 8: bit 1 at weight 256 contributes 256.
  5. Column 7: bit 0 at weight 128 contributes 0.
  6. Column 6: bit 0 at weight 64 contributes 0.
  7. Column 5: bit 1 at weight 32 contributes 32.
  8. Column 4: bit 0 at weight 16 contributes 0.
  9. Column 3: bit 0 at weight 8 contributes 0.
  10. Column 2: bit 0 at weight 4 contributes 0.
  11. Column 1: bit 0 at weight 2 contributes 0.
  12. Column 0: bit 1 at weight 1 contributes 1.
  13. The one-bit weights are 256 + 32 + 1.
  14. Add just the selected weights: 289.
  15. Answer: 100100001₂ = 289₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 289₁₀

Foundations · Problem 0291

Read 100100010₂ 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 9-bit pattern: 100100010.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 9-bit pattern has weight 2^8 = 256.
  4. Column 8: bit 1 at weight 256 contributes 256.
  5. Column 7: bit 0 at weight 128 contributes 0.
  6. Column 6: bit 0 at weight 64 contributes 0.
  7. Column 5: bit 1 at weight 32 contributes 32.
  8. Column 4: bit 0 at weight 16 contributes 0.
  9. Column 3: bit 0 at weight 8 contributes 0.
  10. Column 2: bit 0 at weight 4 contributes 0.
  11. Column 1: bit 1 at weight 2 contributes 2.
  12. Column 0: bit 0 at weight 1 contributes 0.
  13. The one-bit weights are 256 + 32 + 2.
  14. Add just the selected weights: 290.
  15. Answer: 100100010₂ = 290₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 290₁₀

Foundations · Problem 0292

Read 100100011₂ 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 9-bit pattern: 100100011.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 9-bit pattern has weight 2^8 = 256.
  4. Column 8: bit 1 at weight 256 contributes 256.
  5. Column 7: bit 0 at weight 128 contributes 0.
  6. Column 6: bit 0 at weight 64 contributes 0.
  7. Column 5: bit 1 at weight 32 contributes 32.
  8. Column 4: bit 0 at weight 16 contributes 0.
  9. Column 3: bit 0 at weight 8 contributes 0.
  10. Column 2: bit 0 at weight 4 contributes 0.
  11. Column 1: bit 1 at weight 2 contributes 2.
  12. Column 0: bit 1 at weight 1 contributes 1.
  13. The one-bit weights are 256 + 32 + 2 + 1.
  14. Add just the selected weights: 291.
  15. Answer: 100100011₂ = 291₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 291₁₀

Foundations · Problem 0293

Read 100100100₂ 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 9-bit pattern: 100100100.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 9-bit pattern has weight 2^8 = 256.
  4. Column 8: bit 1 at weight 256 contributes 256.
  5. Column 7: bit 0 at weight 128 contributes 0.
  6. Column 6: bit 0 at weight 64 contributes 0.
  7. Column 5: bit 1 at weight 32 contributes 32.
  8. Column 4: bit 0 at weight 16 contributes 0.
  9. Column 3: bit 0 at weight 8 contributes 0.
  10. Column 2: bit 1 at weight 4 contributes 4.
  11. Column 1: bit 0 at weight 2 contributes 0.
  12. Column 0: bit 0 at weight 1 contributes 0.
  13. The one-bit weights are 256 + 32 + 4.
  14. Add just the selected weights: 292.
  15. Answer: 100100100₂ = 292₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 292₁₀

Foundations · Problem 0294

Read 100100101₂ 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 9-bit pattern: 100100101.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 9-bit pattern has weight 2^8 = 256.
  4. Column 8: bit 1 at weight 256 contributes 256.
  5. Column 7: bit 0 at weight 128 contributes 0.
  6. Column 6: bit 0 at weight 64 contributes 0.
  7. Column 5: bit 1 at weight 32 contributes 32.
  8. Column 4: bit 0 at weight 16 contributes 0.
  9. Column 3: bit 0 at weight 8 contributes 0.
  10. Column 2: bit 1 at weight 4 contributes 4.
  11. Column 1: bit 0 at weight 2 contributes 0.
  12. Column 0: bit 1 at weight 1 contributes 1.
  13. The one-bit weights are 256 + 32 + 4 + 1.
  14. Add just the selected weights: 293.
  15. Answer: 100100101₂ = 293₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 293₁₀

Foundations · Problem 0295

Read 100100110₂ 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 9-bit pattern: 100100110.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 9-bit pattern has weight 2^8 = 256.
  4. Column 8: bit 1 at weight 256 contributes 256.
  5. Column 7: bit 0 at weight 128 contributes 0.
  6. Column 6: bit 0 at weight 64 contributes 0.
  7. Column 5: bit 1 at weight 32 contributes 32.
  8. Column 4: bit 0 at weight 16 contributes 0.
  9. Column 3: bit 0 at weight 8 contributes 0.
  10. Column 2: bit 1 at weight 4 contributes 4.
  11. Column 1: bit 1 at weight 2 contributes 2.
  12. Column 0: bit 0 at weight 1 contributes 0.
  13. The one-bit weights are 256 + 32 + 4 + 2.
  14. Add just the selected weights: 294.
  15. Answer: 100100110₂ = 294₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 294₁₀

Foundations · Problem 0296

Read 100100111₂ 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 9-bit pattern: 100100111.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 9-bit pattern has weight 2^8 = 256.
  4. Column 8: bit 1 at weight 256 contributes 256.
  5. Column 7: bit 0 at weight 128 contributes 0.
  6. Column 6: bit 0 at weight 64 contributes 0.
  7. Column 5: bit 1 at weight 32 contributes 32.
  8. Column 4: bit 0 at weight 16 contributes 0.
  9. Column 3: bit 0 at weight 8 contributes 0.
  10. Column 2: bit 1 at weight 4 contributes 4.
  11. Column 1: bit 1 at weight 2 contributes 2.
  12. Column 0: bit 1 at weight 1 contributes 1.
  13. The one-bit weights are 256 + 32 + 4 + 2 + 1.
  14. Add just the selected weights: 295.
  15. Answer: 100100111₂ = 295₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 295₁₀

Foundations · Problem 0297

Read 100101000₂ 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 9-bit pattern: 100101000.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 9-bit pattern has weight 2^8 = 256.
  4. Column 8: bit 1 at weight 256 contributes 256.
  5. Column 7: bit 0 at weight 128 contributes 0.
  6. Column 6: bit 0 at weight 64 contributes 0.
  7. Column 5: bit 1 at weight 32 contributes 32.
  8. Column 4: bit 0 at weight 16 contributes 0.
  9. Column 3: bit 1 at weight 8 contributes 8.
  10. Column 2: bit 0 at weight 4 contributes 0.
  11. Column 1: bit 0 at weight 2 contributes 0.
  12. Column 0: bit 0 at weight 1 contributes 0.
  13. The one-bit weights are 256 + 32 + 8.
  14. Add just the selected weights: 296.
  15. Answer: 100101000₂ = 296₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 296₁₀

Foundations · Problem 0298

Read 100101001₂ 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 9-bit pattern: 100101001.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 9-bit pattern has weight 2^8 = 256.
  4. Column 8: bit 1 at weight 256 contributes 256.
  5. Column 7: bit 0 at weight 128 contributes 0.
  6. Column 6: bit 0 at weight 64 contributes 0.
  7. Column 5: bit 1 at weight 32 contributes 32.
  8. Column 4: bit 0 at weight 16 contributes 0.
  9. Column 3: bit 1 at weight 8 contributes 8.
  10. Column 2: bit 0 at weight 4 contributes 0.
  11. Column 1: bit 0 at weight 2 contributes 0.
  12. Column 0: bit 1 at weight 1 contributes 1.
  13. The one-bit weights are 256 + 32 + 8 + 1.
  14. Add just the selected weights: 297.
  15. Answer: 100101001₂ = 297₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 297₁₀

Foundations · Problem 0299

Read 100101010₂ 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 9-bit pattern: 100101010.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 9-bit pattern has weight 2^8 = 256.
  4. Column 8: bit 1 at weight 256 contributes 256.
  5. Column 7: bit 0 at weight 128 contributes 0.
  6. Column 6: bit 0 at weight 64 contributes 0.
  7. Column 5: bit 1 at weight 32 contributes 32.
  8. Column 4: bit 0 at weight 16 contributes 0.
  9. Column 3: bit 1 at weight 8 contributes 8.
  10. Column 2: bit 0 at weight 4 contributes 0.
  11. Column 1: bit 1 at weight 2 contributes 2.
  12. Column 0: bit 0 at weight 1 contributes 0.
  13. The one-bit weights are 256 + 32 + 8 + 2.
  14. Add just the selected weights: 298.
  15. Answer: 100101010₂ = 298₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 298₁₀

Foundations · Problem 0300

Read 100101011₂ 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 9-bit pattern: 100101011.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 9-bit pattern has weight 2^8 = 256.
  4. Column 8: bit 1 at weight 256 contributes 256.
  5. Column 7: bit 0 at weight 128 contributes 0.
  6. Column 6: bit 0 at weight 64 contributes 0.
  7. Column 5: bit 1 at weight 32 contributes 32.
  8. Column 4: bit 0 at weight 16 contributes 0.
  9. Column 3: bit 1 at weight 8 contributes 8.
  10. Column 2: bit 0 at weight 4 contributes 0.
  11. Column 1: bit 1 at weight 2 contributes 2.
  12. Column 0: bit 1 at weight 1 contributes 1.
  13. The one-bit weights are 256 + 32 + 8 + 2 + 1.
  14. Add just the selected weights: 299.
  15. Answer: 100101011₂ = 299₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 299₁₀

Foundations · Problem 0301

Read 100101100₂ 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 9-bit pattern: 100101100.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 9-bit pattern has weight 2^8 = 256.
  4. Column 8: bit 1 at weight 256 contributes 256.
  5. Column 7: bit 0 at weight 128 contributes 0.
  6. Column 6: bit 0 at weight 64 contributes 0.
  7. Column 5: bit 1 at weight 32 contributes 32.
  8. Column 4: bit 0 at weight 16 contributes 0.
  9. Column 3: bit 1 at weight 8 contributes 8.
  10. Column 2: bit 1 at weight 4 contributes 4.
  11. Column 1: bit 0 at weight 2 contributes 0.
  12. Column 0: bit 0 at weight 1 contributes 0.
  13. The one-bit weights are 256 + 32 + 8 + 4.
  14. Add just the selected weights: 300.
  15. Answer: 100101100₂ = 300₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 300₁₀

Foundations · Problem 0302

Read 100101101₂ 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 9-bit pattern: 100101101.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 9-bit pattern has weight 2^8 = 256.
  4. Column 8: bit 1 at weight 256 contributes 256.
  5. Column 7: bit 0 at weight 128 contributes 0.
  6. Column 6: bit 0 at weight 64 contributes 0.
  7. Column 5: bit 1 at weight 32 contributes 32.
  8. Column 4: bit 0 at weight 16 contributes 0.
  9. Column 3: bit 1 at weight 8 contributes 8.
  10. Column 2: bit 1 at weight 4 contributes 4.
  11. Column 1: bit 0 at weight 2 contributes 0.
  12. Column 0: bit 1 at weight 1 contributes 1.
  13. The one-bit weights are 256 + 32 + 8 + 4 + 1.
  14. Add just the selected weights: 301.
  15. Answer: 100101101₂ = 301₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 301₁₀

Foundations · Problem 0303

Read 100101110₂ 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 9-bit pattern: 100101110.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 9-bit pattern has weight 2^8 = 256.
  4. Column 8: bit 1 at weight 256 contributes 256.
  5. Column 7: bit 0 at weight 128 contributes 0.
  6. Column 6: bit 0 at weight 64 contributes 0.
  7. Column 5: bit 1 at weight 32 contributes 32.
  8. Column 4: bit 0 at weight 16 contributes 0.
  9. Column 3: bit 1 at weight 8 contributes 8.
  10. Column 2: bit 1 at weight 4 contributes 4.
  11. Column 1: bit 1 at weight 2 contributes 2.
  12. Column 0: bit 0 at weight 1 contributes 0.
  13. The one-bit weights are 256 + 32 + 8 + 4 + 2.
  14. Add just the selected weights: 302.
  15. Answer: 100101110₂ = 302₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 302₁₀

Foundations · Problem 0304

Read 100101111₂ 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 9-bit pattern: 100101111.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 9-bit pattern has weight 2^8 = 256.
  4. Column 8: bit 1 at weight 256 contributes 256.
  5. Column 7: bit 0 at weight 128 contributes 0.
  6. Column 6: bit 0 at weight 64 contributes 0.
  7. Column 5: bit 1 at weight 32 contributes 32.
  8. Column 4: bit 0 at weight 16 contributes 0.
  9. Column 3: bit 1 at weight 8 contributes 8.
  10. Column 2: bit 1 at weight 4 contributes 4.
  11. Column 1: bit 1 at weight 2 contributes 2.
  12. Column 0: bit 1 at weight 1 contributes 1.
  13. The one-bit weights are 256 + 32 + 8 + 4 + 2 + 1.
  14. Add just the selected weights: 303.
  15. Answer: 100101111₂ = 303₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 303₁₀

Foundations · Problem 0305

Read 100110000₂ 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 9-bit pattern: 100110000.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 9-bit pattern has weight 2^8 = 256.
  4. Column 8: bit 1 at weight 256 contributes 256.
  5. Column 7: bit 0 at weight 128 contributes 0.
  6. Column 6: bit 0 at weight 64 contributes 0.
  7. Column 5: bit 1 at weight 32 contributes 32.
  8. Column 4: bit 1 at weight 16 contributes 16.
  9. Column 3: bit 0 at weight 8 contributes 0.
  10. Column 2: bit 0 at weight 4 contributes 0.
  11. Column 1: bit 0 at weight 2 contributes 0.
  12. Column 0: bit 0 at weight 1 contributes 0.
  13. The one-bit weights are 256 + 32 + 16.
  14. Add just the selected weights: 304.
  15. Answer: 100110000₂ = 304₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 304₁₀

Foundations · Problem 0306

Read 100110001₂ 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 9-bit pattern: 100110001.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 9-bit pattern has weight 2^8 = 256.
  4. Column 8: bit 1 at weight 256 contributes 256.
  5. Column 7: bit 0 at weight 128 contributes 0.
  6. Column 6: bit 0 at weight 64 contributes 0.
  7. Column 5: bit 1 at weight 32 contributes 32.
  8. Column 4: bit 1 at weight 16 contributes 16.
  9. Column 3: bit 0 at weight 8 contributes 0.
  10. Column 2: bit 0 at weight 4 contributes 0.
  11. Column 1: bit 0 at weight 2 contributes 0.
  12. Column 0: bit 1 at weight 1 contributes 1.
  13. The one-bit weights are 256 + 32 + 16 + 1.
  14. Add just the selected weights: 305.
  15. Answer: 100110001₂ = 305₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 305₁₀

Foundations · Problem 0307

Read 100110010₂ 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 9-bit pattern: 100110010.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 9-bit pattern has weight 2^8 = 256.
  4. Column 8: bit 1 at weight 256 contributes 256.
  5. Column 7: bit 0 at weight 128 contributes 0.
  6. Column 6: bit 0 at weight 64 contributes 0.
  7. Column 5: bit 1 at weight 32 contributes 32.
  8. Column 4: bit 1 at weight 16 contributes 16.
  9. Column 3: bit 0 at weight 8 contributes 0.
  10. Column 2: bit 0 at weight 4 contributes 0.
  11. Column 1: bit 1 at weight 2 contributes 2.
  12. Column 0: bit 0 at weight 1 contributes 0.
  13. The one-bit weights are 256 + 32 + 16 + 2.
  14. Add just the selected weights: 306.
  15. Answer: 100110010₂ = 306₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 306₁₀

Foundations · Problem 0308

Read 100110011₂ 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 9-bit pattern: 100110011.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 9-bit pattern has weight 2^8 = 256.
  4. Column 8: bit 1 at weight 256 contributes 256.
  5. Column 7: bit 0 at weight 128 contributes 0.
  6. Column 6: bit 0 at weight 64 contributes 0.
  7. Column 5: bit 1 at weight 32 contributes 32.
  8. Column 4: bit 1 at weight 16 contributes 16.
  9. Column 3: bit 0 at weight 8 contributes 0.
  10. Column 2: bit 0 at weight 4 contributes 0.
  11. Column 1: bit 1 at weight 2 contributes 2.
  12. Column 0: bit 1 at weight 1 contributes 1.
  13. The one-bit weights are 256 + 32 + 16 + 2 + 1.
  14. Add just the selected weights: 307.
  15. Answer: 100110011₂ = 307₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 307₁₀

Foundations · Problem 0309

Read 100110100₂ 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 9-bit pattern: 100110100.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 9-bit pattern has weight 2^8 = 256.
  4. Column 8: bit 1 at weight 256 contributes 256.
  5. Column 7: bit 0 at weight 128 contributes 0.
  6. Column 6: bit 0 at weight 64 contributes 0.
  7. Column 5: bit 1 at weight 32 contributes 32.
  8. Column 4: bit 1 at weight 16 contributes 16.
  9. Column 3: bit 0 at weight 8 contributes 0.
  10. Column 2: bit 1 at weight 4 contributes 4.
  11. Column 1: bit 0 at weight 2 contributes 0.
  12. Column 0: bit 0 at weight 1 contributes 0.
  13. The one-bit weights are 256 + 32 + 16 + 4.
  14. Add just the selected weights: 308.
  15. Answer: 100110100₂ = 308₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 308₁₀

Foundations · Problem 0310

Read 100110101₂ 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 9-bit pattern: 100110101.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 9-bit pattern has weight 2^8 = 256.
  4. Column 8: bit 1 at weight 256 contributes 256.
  5. Column 7: bit 0 at weight 128 contributes 0.
  6. Column 6: bit 0 at weight 64 contributes 0.
  7. Column 5: bit 1 at weight 32 contributes 32.
  8. Column 4: bit 1 at weight 16 contributes 16.
  9. Column 3: bit 0 at weight 8 contributes 0.
  10. Column 2: bit 1 at weight 4 contributes 4.
  11. Column 1: bit 0 at weight 2 contributes 0.
  12. Column 0: bit 1 at weight 1 contributes 1.
  13. The one-bit weights are 256 + 32 + 16 + 4 + 1.
  14. Add just the selected weights: 309.
  15. Answer: 100110101₂ = 309₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 309₁₀

Foundations · Problem 0311

Read 100110110₂ 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 9-bit pattern: 100110110.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 9-bit pattern has weight 2^8 = 256.
  4. Column 8: bit 1 at weight 256 contributes 256.
  5. Column 7: bit 0 at weight 128 contributes 0.
  6. Column 6: bit 0 at weight 64 contributes 0.
  7. Column 5: bit 1 at weight 32 contributes 32.
  8. Column 4: bit 1 at weight 16 contributes 16.
  9. Column 3: bit 0 at weight 8 contributes 0.
  10. Column 2: bit 1 at weight 4 contributes 4.
  11. Column 1: bit 1 at weight 2 contributes 2.
  12. Column 0: bit 0 at weight 1 contributes 0.
  13. The one-bit weights are 256 + 32 + 16 + 4 + 2.
  14. Add just the selected weights: 310.
  15. Answer: 100110110₂ = 310₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 310₁₀

Foundations · Problem 0312

Read 100110111₂ 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 9-bit pattern: 100110111.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 9-bit pattern has weight 2^8 = 256.
  4. Column 8: bit 1 at weight 256 contributes 256.
  5. Column 7: bit 0 at weight 128 contributes 0.
  6. Column 6: bit 0 at weight 64 contributes 0.
  7. Column 5: bit 1 at weight 32 contributes 32.
  8. Column 4: bit 1 at weight 16 contributes 16.
  9. Column 3: bit 0 at weight 8 contributes 0.
  10. Column 2: bit 1 at weight 4 contributes 4.
  11. Column 1: bit 1 at weight 2 contributes 2.
  12. Column 0: bit 1 at weight 1 contributes 1.
  13. The one-bit weights are 256 + 32 + 16 + 4 + 2 + 1.
  14. Add just the selected weights: 311.
  15. Answer: 100110111₂ = 311₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 311₁₀

Foundations · Problem 0313

Read 100111000₂ 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 9-bit pattern: 100111000.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 9-bit pattern has weight 2^8 = 256.
  4. Column 8: bit 1 at weight 256 contributes 256.
  5. Column 7: bit 0 at weight 128 contributes 0.
  6. Column 6: bit 0 at weight 64 contributes 0.
  7. Column 5: bit 1 at weight 32 contributes 32.
  8. Column 4: bit 1 at weight 16 contributes 16.
  9. Column 3: bit 1 at weight 8 contributes 8.
  10. Column 2: bit 0 at weight 4 contributes 0.
  11. Column 1: bit 0 at weight 2 contributes 0.
  12. Column 0: bit 0 at weight 1 contributes 0.
  13. The one-bit weights are 256 + 32 + 16 + 8.
  14. Add just the selected weights: 312.
  15. Answer: 100111000₂ = 312₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 312₁₀

Foundations · Problem 0314

Read 100111001₂ 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 9-bit pattern: 100111001.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 9-bit pattern has weight 2^8 = 256.
  4. Column 8: bit 1 at weight 256 contributes 256.
  5. Column 7: bit 0 at weight 128 contributes 0.
  6. Column 6: bit 0 at weight 64 contributes 0.
  7. Column 5: bit 1 at weight 32 contributes 32.
  8. Column 4: bit 1 at weight 16 contributes 16.
  9. Column 3: bit 1 at weight 8 contributes 8.
  10. Column 2: bit 0 at weight 4 contributes 0.
  11. Column 1: bit 0 at weight 2 contributes 0.
  12. Column 0: bit 1 at weight 1 contributes 1.
  13. The one-bit weights are 256 + 32 + 16 + 8 + 1.
  14. Add just the selected weights: 313.
  15. Answer: 100111001₂ = 313₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 313₁₀

Foundations · Problem 0315

Read 100111010₂ 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 9-bit pattern: 100111010.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 9-bit pattern has weight 2^8 = 256.
  4. Column 8: bit 1 at weight 256 contributes 256.
  5. Column 7: bit 0 at weight 128 contributes 0.
  6. Column 6: bit 0 at weight 64 contributes 0.
  7. Column 5: bit 1 at weight 32 contributes 32.
  8. Column 4: bit 1 at weight 16 contributes 16.
  9. Column 3: bit 1 at weight 8 contributes 8.
  10. Column 2: bit 0 at weight 4 contributes 0.
  11. Column 1: bit 1 at weight 2 contributes 2.
  12. Column 0: bit 0 at weight 1 contributes 0.
  13. The one-bit weights are 256 + 32 + 16 + 8 + 2.
  14. Add just the selected weights: 314.
  15. Answer: 100111010₂ = 314₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 314₁₀

Foundations · Problem 0316

Read 100111011₂ 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 9-bit pattern: 100111011.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 9-bit pattern has weight 2^8 = 256.
  4. Column 8: bit 1 at weight 256 contributes 256.
  5. Column 7: bit 0 at weight 128 contributes 0.
  6. Column 6: bit 0 at weight 64 contributes 0.
  7. Column 5: bit 1 at weight 32 contributes 32.
  8. Column 4: bit 1 at weight 16 contributes 16.
  9. Column 3: bit 1 at weight 8 contributes 8.
  10. Column 2: bit 0 at weight 4 contributes 0.
  11. Column 1: bit 1 at weight 2 contributes 2.
  12. Column 0: bit 1 at weight 1 contributes 1.
  13. The one-bit weights are 256 + 32 + 16 + 8 + 2 + 1.
  14. Add just the selected weights: 315.
  15. Answer: 100111011₂ = 315₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 315₁₀

Foundations · Problem 0317

Read 100111100₂ 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 9-bit pattern: 100111100.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 9-bit pattern has weight 2^8 = 256.
  4. Column 8: bit 1 at weight 256 contributes 256.
  5. Column 7: bit 0 at weight 128 contributes 0.
  6. Column 6: bit 0 at weight 64 contributes 0.
  7. Column 5: bit 1 at weight 32 contributes 32.
  8. Column 4: bit 1 at weight 16 contributes 16.
  9. Column 3: bit 1 at weight 8 contributes 8.
  10. Column 2: bit 1 at weight 4 contributes 4.
  11. Column 1: bit 0 at weight 2 contributes 0.
  12. Column 0: bit 0 at weight 1 contributes 0.
  13. The one-bit weights are 256 + 32 + 16 + 8 + 4.
  14. Add just the selected weights: 316.
  15. Answer: 100111100₂ = 316₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 316₁₀

Foundations · Problem 0318

Read 100111101₂ 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 9-bit pattern: 100111101.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 9-bit pattern has weight 2^8 = 256.
  4. Column 8: bit 1 at weight 256 contributes 256.
  5. Column 7: bit 0 at weight 128 contributes 0.
  6. Column 6: bit 0 at weight 64 contributes 0.
  7. Column 5: bit 1 at weight 32 contributes 32.
  8. Column 4: bit 1 at weight 16 contributes 16.
  9. Column 3: bit 1 at weight 8 contributes 8.
  10. Column 2: bit 1 at weight 4 contributes 4.
  11. Column 1: bit 0 at weight 2 contributes 0.
  12. Column 0: bit 1 at weight 1 contributes 1.
  13. The one-bit weights are 256 + 32 + 16 + 8 + 4 + 1.
  14. Add just the selected weights: 317.
  15. Answer: 100111101₂ = 317₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 317₁₀

Foundations · Problem 0319

Read 100111110₂ 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 9-bit pattern: 100111110.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 9-bit pattern has weight 2^8 = 256.
  4. Column 8: bit 1 at weight 256 contributes 256.
  5. Column 7: bit 0 at weight 128 contributes 0.
  6. Column 6: bit 0 at weight 64 contributes 0.
  7. Column 5: bit 1 at weight 32 contributes 32.
  8. Column 4: bit 1 at weight 16 contributes 16.
  9. Column 3: bit 1 at weight 8 contributes 8.
  10. Column 2: bit 1 at weight 4 contributes 4.
  11. Column 1: bit 1 at weight 2 contributes 2.
  12. Column 0: bit 0 at weight 1 contributes 0.
  13. The one-bit weights are 256 + 32 + 16 + 8 + 4 + 2.
  14. Add just the selected weights: 318.
  15. Answer: 100111110₂ = 318₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 318₁₀

Foundations · Problem 0320

Read 100111111₂ 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 9-bit pattern: 100111111.
  2. The rightmost bit has weight 2⁰ = 1; every move left doubles the weight.
  3. The leftmost bit in this 9-bit pattern has weight 2^8 = 256.
  4. Column 8: bit 1 at weight 256 contributes 256.
  5. Column 7: bit 0 at weight 128 contributes 0.
  6. Column 6: bit 0 at weight 64 contributes 0.
  7. Column 5: bit 1 at weight 32 contributes 32.
  8. Column 4: bit 1 at weight 16 contributes 16.
  9. Column 3: bit 1 at weight 8 contributes 8.
  10. Column 2: bit 1 at weight 4 contributes 4.
  11. Column 1: bit 1 at weight 2 contributes 2.
  12. Column 0: bit 1 at weight 1 contributes 1.
  13. The one-bit weights are 256 + 32 + 16 + 8 + 4 + 2 + 1.
  14. Add just the selected weights: 319.
  15. Answer: 100111111₂ = 319₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 319₁₀