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Reading binary

Set 9 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 0257

Read 100000000₂ 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: 100000000.
  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 0 at weight 32 contributes 0.
  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.
  14. Add just the selected weights: 256.
  15. Answer: 100000000₂ = 256₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 256₁₀

Foundations · Problem 0258

Read 100000001₂ 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: 100000001.
  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 0 at weight 32 contributes 0.
  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 + 1.
  14. Add just the selected weights: 257.
  15. Answer: 100000001₂ = 257₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 257₁₀

Foundations · Problem 0259

Read 100000010₂ 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: 100000010.
  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 0 at weight 32 contributes 0.
  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 + 2.
  14. Add just the selected weights: 258.
  15. Answer: 100000010₂ = 258₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 258₁₀

Foundations · Problem 0260

Read 100000011₂ 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: 100000011.
  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 0 at weight 32 contributes 0.
  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 + 2 + 1.
  14. Add just the selected weights: 259.
  15. Answer: 100000011₂ = 259₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 259₁₀

Foundations · Problem 0261

Read 100000100₂ 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: 100000100.
  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 0 at weight 32 contributes 0.
  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 + 4.
  14. Add just the selected weights: 260.
  15. Answer: 100000100₂ = 260₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 260₁₀

Foundations · Problem 0262

Read 100000101₂ 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: 100000101.
  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 0 at weight 32 contributes 0.
  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 + 4 + 1.
  14. Add just the selected weights: 261.
  15. Answer: 100000101₂ = 261₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 261₁₀

Foundations · Problem 0263

Read 100000110₂ 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: 100000110.
  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 0 at weight 32 contributes 0.
  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 + 4 + 2.
  14. Add just the selected weights: 262.
  15. Answer: 100000110₂ = 262₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 262₁₀

Foundations · Problem 0264

Read 100000111₂ 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: 100000111.
  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 0 at weight 32 contributes 0.
  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 + 4 + 2 + 1.
  14. Add just the selected weights: 263.
  15. Answer: 100000111₂ = 263₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 263₁₀

Foundations · Problem 0265

Read 100001000₂ 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: 100001000.
  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 0 at weight 32 contributes 0.
  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 + 8.
  14. Add just the selected weights: 264.
  15. Answer: 100001000₂ = 264₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 264₁₀

Foundations · Problem 0266

Read 100001001₂ 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: 100001001.
  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 0 at weight 32 contributes 0.
  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 + 8 + 1.
  14. Add just the selected weights: 265.
  15. Answer: 100001001₂ = 265₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 265₁₀

Foundations · Problem 0267

Read 100001010₂ 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: 100001010.
  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 0 at weight 32 contributes 0.
  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 + 8 + 2.
  14. Add just the selected weights: 266.
  15. Answer: 100001010₂ = 266₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 266₁₀

Foundations · Problem 0268

Read 100001011₂ 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: 100001011.
  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 0 at weight 32 contributes 0.
  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 + 8 + 2 + 1.
  14. Add just the selected weights: 267.
  15. Answer: 100001011₂ = 267₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 267₁₀

Foundations · Problem 0269

Read 100001100₂ 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: 100001100.
  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 0 at weight 32 contributes 0.
  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 + 8 + 4.
  14. Add just the selected weights: 268.
  15. Answer: 100001100₂ = 268₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 268₁₀

Foundations · Problem 0270

Read 100001101₂ 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: 100001101.
  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 0 at weight 32 contributes 0.
  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 + 8 + 4 + 1.
  14. Add just the selected weights: 269.
  15. Answer: 100001101₂ = 269₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 269₁₀

Foundations · Problem 0271

Read 100001110₂ 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: 100001110.
  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 0 at weight 32 contributes 0.
  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 + 8 + 4 + 2.
  14. Add just the selected weights: 270.
  15. Answer: 100001110₂ = 270₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 270₁₀

Foundations · Problem 0272

Read 100001111₂ 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: 100001111.
  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 0 at weight 32 contributes 0.
  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 + 8 + 4 + 2 + 1.
  14. Add just the selected weights: 271.
  15. Answer: 100001111₂ = 271₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 271₁₀

Foundations · Problem 0273

Read 100010000₂ 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: 100010000.
  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 0 at weight 32 contributes 0.
  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 + 16.
  14. Add just the selected weights: 272.
  15. Answer: 100010000₂ = 272₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 272₁₀

Foundations · Problem 0274

Read 100010001₂ 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: 100010001.
  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 0 at weight 32 contributes 0.
  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 + 16 + 1.
  14. Add just the selected weights: 273.
  15. Answer: 100010001₂ = 273₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 273₁₀

Foundations · Problem 0275

Read 100010010₂ 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: 100010010.
  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 0 at weight 32 contributes 0.
  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 + 16 + 2.
  14. Add just the selected weights: 274.
  15. Answer: 100010010₂ = 274₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 274₁₀

Foundations · Problem 0276

Read 100010011₂ 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: 100010011.
  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 0 at weight 32 contributes 0.
  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 + 16 + 2 + 1.
  14. Add just the selected weights: 275.
  15. Answer: 100010011₂ = 275₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 275₁₀

Foundations · Problem 0277

Read 100010100₂ 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: 100010100.
  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 0 at weight 32 contributes 0.
  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 + 16 + 4.
  14. Add just the selected weights: 276.
  15. Answer: 100010100₂ = 276₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 276₁₀

Foundations · Problem 0278

Read 100010101₂ 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: 100010101.
  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 0 at weight 32 contributes 0.
  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 + 16 + 4 + 1.
  14. Add just the selected weights: 277.
  15. Answer: 100010101₂ = 277₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 277₁₀

Foundations · Problem 0279

Read 100010110₂ 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: 100010110.
  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 0 at weight 32 contributes 0.
  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 + 16 + 4 + 2.
  14. Add just the selected weights: 278.
  15. Answer: 100010110₂ = 278₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 278₁₀

Foundations · Problem 0280

Read 100010111₂ 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: 100010111.
  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 0 at weight 32 contributes 0.
  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 + 16 + 4 + 2 + 1.
  14. Add just the selected weights: 279.
  15. Answer: 100010111₂ = 279₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 279₁₀

Foundations · Problem 0281

Read 100011000₂ 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: 100011000.
  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 0 at weight 32 contributes 0.
  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 + 16 + 8.
  14. Add just the selected weights: 280.
  15. Answer: 100011000₂ = 280₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 280₁₀

Foundations · Problem 0282

Read 100011001₂ 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: 100011001.
  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 0 at weight 32 contributes 0.
  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 + 16 + 8 + 1.
  14. Add just the selected weights: 281.
  15. Answer: 100011001₂ = 281₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 281₁₀

Foundations · Problem 0283

Read 100011010₂ 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: 100011010.
  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 0 at weight 32 contributes 0.
  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 + 16 + 8 + 2.
  14. Add just the selected weights: 282.
  15. Answer: 100011010₂ = 282₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 282₁₀

Foundations · Problem 0284

Read 100011011₂ 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: 100011011.
  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 0 at weight 32 contributes 0.
  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 + 16 + 8 + 2 + 1.
  14. Add just the selected weights: 283.
  15. Answer: 100011011₂ = 283₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 283₁₀

Foundations · Problem 0285

Read 100011100₂ 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: 100011100.
  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 0 at weight 32 contributes 0.
  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 + 16 + 8 + 4.
  14. Add just the selected weights: 284.
  15. Answer: 100011100₂ = 284₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 284₁₀

Foundations · Problem 0286

Read 100011101₂ 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: 100011101.
  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 0 at weight 32 contributes 0.
  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 + 16 + 8 + 4 + 1.
  14. Add just the selected weights: 285.
  15. Answer: 100011101₂ = 285₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 285₁₀

Foundations · Problem 0287

Read 100011110₂ 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: 100011110.
  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 0 at weight 32 contributes 0.
  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 + 16 + 8 + 4 + 2.
  14. Add just the selected weights: 286.
  15. Answer: 100011110₂ = 286₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 286₁₀

Foundations · Problem 0288

Read 100011111₂ 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: 100011111.
  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 0 at weight 32 contributes 0.
  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 + 16 + 8 + 4 + 2 + 1.
  14. Add just the selected weights: 287.
  15. Answer: 100011111₂ = 287₁₀.
  16. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 287₁₀