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Reading binary

Set 8 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 0225

Read 11100000₂ 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: 11100000.
  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 1 at weight 128 contributes 128.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 1 at weight 32 contributes 32.
  7. Column 4: bit 0 at weight 16 contributes 0.
  8. Column 3: bit 0 at weight 8 contributes 0.
  9. Column 2: bit 0 at weight 4 contributes 0.
  10. Column 1: bit 0 at weight 2 contributes 0.
  11. Column 0: bit 0 at weight 1 contributes 0.
  12. The one-bit weights are 128 + 64 + 32.
  13. Add just the selected weights: 224.
  14. Answer: 11100000₂ = 224₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 224₁₀

Foundations · Problem 0226

Read 11100001₂ 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: 11100001.
  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 1 at weight 128 contributes 128.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 1 at weight 32 contributes 32.
  7. Column 4: bit 0 at weight 16 contributes 0.
  8. Column 3: bit 0 at weight 8 contributes 0.
  9. Column 2: bit 0 at weight 4 contributes 0.
  10. Column 1: bit 0 at weight 2 contributes 0.
  11. Column 0: bit 1 at weight 1 contributes 1.
  12. The one-bit weights are 128 + 64 + 32 + 1.
  13. Add just the selected weights: 225.
  14. Answer: 11100001₂ = 225₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 225₁₀

Foundations · Problem 0227

Read 11100010₂ 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: 11100010.
  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 1 at weight 128 contributes 128.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 1 at weight 32 contributes 32.
  7. Column 4: bit 0 at weight 16 contributes 0.
  8. Column 3: bit 0 at weight 8 contributes 0.
  9. Column 2: bit 0 at weight 4 contributes 0.
  10. Column 1: bit 1 at weight 2 contributes 2.
  11. Column 0: bit 0 at weight 1 contributes 0.
  12. The one-bit weights are 128 + 64 + 32 + 2.
  13. Add just the selected weights: 226.
  14. Answer: 11100010₂ = 226₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 226₁₀

Foundations · Problem 0228

Read 11100011₂ 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: 11100011.
  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 1 at weight 128 contributes 128.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 1 at weight 32 contributes 32.
  7. Column 4: bit 0 at weight 16 contributes 0.
  8. Column 3: bit 0 at weight 8 contributes 0.
  9. Column 2: bit 0 at weight 4 contributes 0.
  10. Column 1: bit 1 at weight 2 contributes 2.
  11. Column 0: bit 1 at weight 1 contributes 1.
  12. The one-bit weights are 128 + 64 + 32 + 2 + 1.
  13. Add just the selected weights: 227.
  14. Answer: 11100011₂ = 227₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 227₁₀

Foundations · Problem 0229

Read 11100100₂ 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: 11100100.
  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 1 at weight 128 contributes 128.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 1 at weight 32 contributes 32.
  7. Column 4: bit 0 at weight 16 contributes 0.
  8. Column 3: bit 0 at weight 8 contributes 0.
  9. Column 2: bit 1 at weight 4 contributes 4.
  10. Column 1: bit 0 at weight 2 contributes 0.
  11. Column 0: bit 0 at weight 1 contributes 0.
  12. The one-bit weights are 128 + 64 + 32 + 4.
  13. Add just the selected weights: 228.
  14. Answer: 11100100₂ = 228₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 228₁₀

Foundations · Problem 0230

Read 11100101₂ 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: 11100101.
  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 1 at weight 128 contributes 128.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 1 at weight 32 contributes 32.
  7. Column 4: bit 0 at weight 16 contributes 0.
  8. Column 3: bit 0 at weight 8 contributes 0.
  9. Column 2: bit 1 at weight 4 contributes 4.
  10. Column 1: bit 0 at weight 2 contributes 0.
  11. Column 0: bit 1 at weight 1 contributes 1.
  12. The one-bit weights are 128 + 64 + 32 + 4 + 1.
  13. Add just the selected weights: 229.
  14. Answer: 11100101₂ = 229₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 229₁₀

Foundations · Problem 0231

Read 11100110₂ 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: 11100110.
  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 1 at weight 128 contributes 128.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 1 at weight 32 contributes 32.
  7. Column 4: bit 0 at weight 16 contributes 0.
  8. Column 3: bit 0 at weight 8 contributes 0.
  9. Column 2: bit 1 at weight 4 contributes 4.
  10. Column 1: bit 1 at weight 2 contributes 2.
  11. Column 0: bit 0 at weight 1 contributes 0.
  12. The one-bit weights are 128 + 64 + 32 + 4 + 2.
  13. Add just the selected weights: 230.
  14. Answer: 11100110₂ = 230₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 230₁₀

Foundations · Problem 0232

Read 11100111₂ 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: 11100111.
  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 1 at weight 128 contributes 128.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 1 at weight 32 contributes 32.
  7. Column 4: bit 0 at weight 16 contributes 0.
  8. Column 3: bit 0 at weight 8 contributes 0.
  9. Column 2: bit 1 at weight 4 contributes 4.
  10. Column 1: bit 1 at weight 2 contributes 2.
  11. Column 0: bit 1 at weight 1 contributes 1.
  12. The one-bit weights are 128 + 64 + 32 + 4 + 2 + 1.
  13. Add just the selected weights: 231.
  14. Answer: 11100111₂ = 231₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 231₁₀

Foundations · Problem 0233

Read 11101000₂ 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: 11101000.
  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 1 at weight 128 contributes 128.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 1 at weight 32 contributes 32.
  7. Column 4: bit 0 at weight 16 contributes 0.
  8. Column 3: bit 1 at weight 8 contributes 8.
  9. Column 2: bit 0 at weight 4 contributes 0.
  10. Column 1: bit 0 at weight 2 contributes 0.
  11. Column 0: bit 0 at weight 1 contributes 0.
  12. The one-bit weights are 128 + 64 + 32 + 8.
  13. Add just the selected weights: 232.
  14. Answer: 11101000₂ = 232₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 232₁₀

Foundations · Problem 0234

Read 11101001₂ 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: 11101001.
  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 1 at weight 128 contributes 128.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 1 at weight 32 contributes 32.
  7. Column 4: bit 0 at weight 16 contributes 0.
  8. Column 3: bit 1 at weight 8 contributes 8.
  9. Column 2: bit 0 at weight 4 contributes 0.
  10. Column 1: bit 0 at weight 2 contributes 0.
  11. Column 0: bit 1 at weight 1 contributes 1.
  12. The one-bit weights are 128 + 64 + 32 + 8 + 1.
  13. Add just the selected weights: 233.
  14. Answer: 11101001₂ = 233₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 233₁₀

Foundations · Problem 0235

Read 11101010₂ 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: 11101010.
  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 1 at weight 128 contributes 128.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 1 at weight 32 contributes 32.
  7. Column 4: bit 0 at weight 16 contributes 0.
  8. Column 3: bit 1 at weight 8 contributes 8.
  9. Column 2: bit 0 at weight 4 contributes 0.
  10. Column 1: bit 1 at weight 2 contributes 2.
  11. Column 0: bit 0 at weight 1 contributes 0.
  12. The one-bit weights are 128 + 64 + 32 + 8 + 2.
  13. Add just the selected weights: 234.
  14. Answer: 11101010₂ = 234₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 234₁₀

Foundations · Problem 0236

Read 11101011₂ 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: 11101011.
  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 1 at weight 128 contributes 128.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 1 at weight 32 contributes 32.
  7. Column 4: bit 0 at weight 16 contributes 0.
  8. Column 3: bit 1 at weight 8 contributes 8.
  9. Column 2: bit 0 at weight 4 contributes 0.
  10. Column 1: bit 1 at weight 2 contributes 2.
  11. Column 0: bit 1 at weight 1 contributes 1.
  12. The one-bit weights are 128 + 64 + 32 + 8 + 2 + 1.
  13. Add just the selected weights: 235.
  14. Answer: 11101011₂ = 235₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 235₁₀

Foundations · Problem 0237

Read 11101100₂ 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: 11101100.
  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 1 at weight 128 contributes 128.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 1 at weight 32 contributes 32.
  7. Column 4: bit 0 at weight 16 contributes 0.
  8. Column 3: bit 1 at weight 8 contributes 8.
  9. Column 2: bit 1 at weight 4 contributes 4.
  10. Column 1: bit 0 at weight 2 contributes 0.
  11. Column 0: bit 0 at weight 1 contributes 0.
  12. The one-bit weights are 128 + 64 + 32 + 8 + 4.
  13. Add just the selected weights: 236.
  14. Answer: 11101100₂ = 236₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 236₁₀

Foundations · Problem 0238

Read 11101101₂ 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: 11101101.
  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 1 at weight 128 contributes 128.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 1 at weight 32 contributes 32.
  7. Column 4: bit 0 at weight 16 contributes 0.
  8. Column 3: bit 1 at weight 8 contributes 8.
  9. Column 2: bit 1 at weight 4 contributes 4.
  10. Column 1: bit 0 at weight 2 contributes 0.
  11. Column 0: bit 1 at weight 1 contributes 1.
  12. The one-bit weights are 128 + 64 + 32 + 8 + 4 + 1.
  13. Add just the selected weights: 237.
  14. Answer: 11101101₂ = 237₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 237₁₀

Foundations · Problem 0239

Read 11101110₂ 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: 11101110.
  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 1 at weight 128 contributes 128.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 1 at weight 32 contributes 32.
  7. Column 4: bit 0 at weight 16 contributes 0.
  8. Column 3: bit 1 at weight 8 contributes 8.
  9. Column 2: bit 1 at weight 4 contributes 4.
  10. Column 1: bit 1 at weight 2 contributes 2.
  11. Column 0: bit 0 at weight 1 contributes 0.
  12. The one-bit weights are 128 + 64 + 32 + 8 + 4 + 2.
  13. Add just the selected weights: 238.
  14. Answer: 11101110₂ = 238₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 238₁₀

Foundations · Problem 0240

Read 11101111₂ 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: 11101111.
  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 1 at weight 128 contributes 128.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 1 at weight 32 contributes 32.
  7. Column 4: bit 0 at weight 16 contributes 0.
  8. Column 3: bit 1 at weight 8 contributes 8.
  9. Column 2: bit 1 at weight 4 contributes 4.
  10. Column 1: bit 1 at weight 2 contributes 2.
  11. Column 0: bit 1 at weight 1 contributes 1.
  12. The one-bit weights are 128 + 64 + 32 + 8 + 4 + 2 + 1.
  13. Add just the selected weights: 239.
  14. Answer: 11101111₂ = 239₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 239₁₀

Foundations · Problem 0241

Read 11110000₂ 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: 11110000.
  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 1 at weight 128 contributes 128.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 1 at weight 32 contributes 32.
  7. Column 4: bit 1 at weight 16 contributes 16.
  8. Column 3: bit 0 at weight 8 contributes 0.
  9. Column 2: bit 0 at weight 4 contributes 0.
  10. Column 1: bit 0 at weight 2 contributes 0.
  11. Column 0: bit 0 at weight 1 contributes 0.
  12. The one-bit weights are 128 + 64 + 32 + 16.
  13. Add just the selected weights: 240.
  14. Answer: 11110000₂ = 240₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 240₁₀

Foundations · Problem 0242

Read 11110001₂ 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: 11110001.
  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 1 at weight 128 contributes 128.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 1 at weight 32 contributes 32.
  7. Column 4: bit 1 at weight 16 contributes 16.
  8. Column 3: bit 0 at weight 8 contributes 0.
  9. Column 2: bit 0 at weight 4 contributes 0.
  10. Column 1: bit 0 at weight 2 contributes 0.
  11. Column 0: bit 1 at weight 1 contributes 1.
  12. The one-bit weights are 128 + 64 + 32 + 16 + 1.
  13. Add just the selected weights: 241.
  14. Answer: 11110001₂ = 241₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 241₁₀

Foundations · Problem 0243

Read 11110010₂ 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: 11110010.
  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 1 at weight 128 contributes 128.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 1 at weight 32 contributes 32.
  7. Column 4: bit 1 at weight 16 contributes 16.
  8. Column 3: bit 0 at weight 8 contributes 0.
  9. Column 2: bit 0 at weight 4 contributes 0.
  10. Column 1: bit 1 at weight 2 contributes 2.
  11. Column 0: bit 0 at weight 1 contributes 0.
  12. The one-bit weights are 128 + 64 + 32 + 16 + 2.
  13. Add just the selected weights: 242.
  14. Answer: 11110010₂ = 242₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 242₁₀

Foundations · Problem 0244

Read 11110011₂ 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: 11110011.
  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 1 at weight 128 contributes 128.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 1 at weight 32 contributes 32.
  7. Column 4: bit 1 at weight 16 contributes 16.
  8. Column 3: bit 0 at weight 8 contributes 0.
  9. Column 2: bit 0 at weight 4 contributes 0.
  10. Column 1: bit 1 at weight 2 contributes 2.
  11. Column 0: bit 1 at weight 1 contributes 1.
  12. The one-bit weights are 128 + 64 + 32 + 16 + 2 + 1.
  13. Add just the selected weights: 243.
  14. Answer: 11110011₂ = 243₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 243₁₀

Foundations · Problem 0245

Read 11110100₂ 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: 11110100.
  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 1 at weight 128 contributes 128.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 1 at weight 32 contributes 32.
  7. Column 4: bit 1 at weight 16 contributes 16.
  8. Column 3: bit 0 at weight 8 contributes 0.
  9. Column 2: bit 1 at weight 4 contributes 4.
  10. Column 1: bit 0 at weight 2 contributes 0.
  11. Column 0: bit 0 at weight 1 contributes 0.
  12. The one-bit weights are 128 + 64 + 32 + 16 + 4.
  13. Add just the selected weights: 244.
  14. Answer: 11110100₂ = 244₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 244₁₀

Foundations · Problem 0246

Read 11110101₂ 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: 11110101.
  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 1 at weight 128 contributes 128.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 1 at weight 32 contributes 32.
  7. Column 4: bit 1 at weight 16 contributes 16.
  8. Column 3: bit 0 at weight 8 contributes 0.
  9. Column 2: bit 1 at weight 4 contributes 4.
  10. Column 1: bit 0 at weight 2 contributes 0.
  11. Column 0: bit 1 at weight 1 contributes 1.
  12. The one-bit weights are 128 + 64 + 32 + 16 + 4 + 1.
  13. Add just the selected weights: 245.
  14. Answer: 11110101₂ = 245₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 245₁₀

Foundations · Problem 0247

Read 11110110₂ 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: 11110110.
  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 1 at weight 128 contributes 128.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 1 at weight 32 contributes 32.
  7. Column 4: bit 1 at weight 16 contributes 16.
  8. Column 3: bit 0 at weight 8 contributes 0.
  9. Column 2: bit 1 at weight 4 contributes 4.
  10. Column 1: bit 1 at weight 2 contributes 2.
  11. Column 0: bit 0 at weight 1 contributes 0.
  12. The one-bit weights are 128 + 64 + 32 + 16 + 4 + 2.
  13. Add just the selected weights: 246.
  14. Answer: 11110110₂ = 246₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 246₁₀

Foundations · Problem 0248

Read 11110111₂ 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: 11110111.
  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 1 at weight 128 contributes 128.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 1 at weight 32 contributes 32.
  7. Column 4: bit 1 at weight 16 contributes 16.
  8. Column 3: bit 0 at weight 8 contributes 0.
  9. Column 2: bit 1 at weight 4 contributes 4.
  10. Column 1: bit 1 at weight 2 contributes 2.
  11. Column 0: bit 1 at weight 1 contributes 1.
  12. The one-bit weights are 128 + 64 + 32 + 16 + 4 + 2 + 1.
  13. Add just the selected weights: 247.
  14. Answer: 11110111₂ = 247₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 247₁₀

Foundations · Problem 0249

Read 11111000₂ 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: 11111000.
  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 1 at weight 128 contributes 128.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 1 at weight 32 contributes 32.
  7. Column 4: bit 1 at weight 16 contributes 16.
  8. Column 3: bit 1 at weight 8 contributes 8.
  9. Column 2: bit 0 at weight 4 contributes 0.
  10. Column 1: bit 0 at weight 2 contributes 0.
  11. Column 0: bit 0 at weight 1 contributes 0.
  12. The one-bit weights are 128 + 64 + 32 + 16 + 8.
  13. Add just the selected weights: 248.
  14. Answer: 11111000₂ = 248₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 248₁₀

Foundations · Problem 0250

Read 11111001₂ 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: 11111001.
  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 1 at weight 128 contributes 128.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 1 at weight 32 contributes 32.
  7. Column 4: bit 1 at weight 16 contributes 16.
  8. Column 3: bit 1 at weight 8 contributes 8.
  9. Column 2: bit 0 at weight 4 contributes 0.
  10. Column 1: bit 0 at weight 2 contributes 0.
  11. Column 0: bit 1 at weight 1 contributes 1.
  12. The one-bit weights are 128 + 64 + 32 + 16 + 8 + 1.
  13. Add just the selected weights: 249.
  14. Answer: 11111001₂ = 249₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 249₁₀

Foundations · Problem 0251

Read 11111010₂ 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: 11111010.
  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 1 at weight 128 contributes 128.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 1 at weight 32 contributes 32.
  7. Column 4: bit 1 at weight 16 contributes 16.
  8. Column 3: bit 1 at weight 8 contributes 8.
  9. Column 2: bit 0 at weight 4 contributes 0.
  10. Column 1: bit 1 at weight 2 contributes 2.
  11. Column 0: bit 0 at weight 1 contributes 0.
  12. The one-bit weights are 128 + 64 + 32 + 16 + 8 + 2.
  13. Add just the selected weights: 250.
  14. Answer: 11111010₂ = 250₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 250₁₀

Foundations · Problem 0252

Read 11111011₂ 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: 11111011.
  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 1 at weight 128 contributes 128.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 1 at weight 32 contributes 32.
  7. Column 4: bit 1 at weight 16 contributes 16.
  8. Column 3: bit 1 at weight 8 contributes 8.
  9. Column 2: bit 0 at weight 4 contributes 0.
  10. Column 1: bit 1 at weight 2 contributes 2.
  11. Column 0: bit 1 at weight 1 contributes 1.
  12. The one-bit weights are 128 + 64 + 32 + 16 + 8 + 2 + 1.
  13. Add just the selected weights: 251.
  14. Answer: 11111011₂ = 251₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 251₁₀

Foundations · Problem 0253

Read 11111100₂ 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: 11111100.
  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 1 at weight 128 contributes 128.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 1 at weight 32 contributes 32.
  7. Column 4: bit 1 at weight 16 contributes 16.
  8. Column 3: bit 1 at weight 8 contributes 8.
  9. Column 2: bit 1 at weight 4 contributes 4.
  10. Column 1: bit 0 at weight 2 contributes 0.
  11. Column 0: bit 0 at weight 1 contributes 0.
  12. The one-bit weights are 128 + 64 + 32 + 16 + 8 + 4.
  13. Add just the selected weights: 252.
  14. Answer: 11111100₂ = 252₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 252₁₀

Foundations · Problem 0254

Read 11111101₂ 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: 11111101.
  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 1 at weight 128 contributes 128.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 1 at weight 32 contributes 32.
  7. Column 4: bit 1 at weight 16 contributes 16.
  8. Column 3: bit 1 at weight 8 contributes 8.
  9. Column 2: bit 1 at weight 4 contributes 4.
  10. Column 1: bit 0 at weight 2 contributes 0.
  11. Column 0: bit 1 at weight 1 contributes 1.
  12. The one-bit weights are 128 + 64 + 32 + 16 + 8 + 4 + 1.
  13. Add just the selected weights: 253.
  14. Answer: 11111101₂ = 253₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 253₁₀

Foundations · Problem 0255

Read 11111110₂ 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: 11111110.
  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 1 at weight 128 contributes 128.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 1 at weight 32 contributes 32.
  7. Column 4: bit 1 at weight 16 contributes 16.
  8. Column 3: bit 1 at weight 8 contributes 8.
  9. Column 2: bit 1 at weight 4 contributes 4.
  10. Column 1: bit 1 at weight 2 contributes 2.
  11. Column 0: bit 0 at weight 1 contributes 0.
  12. The one-bit weights are 128 + 64 + 32 + 16 + 8 + 4 + 2.
  13. Add just the selected weights: 254.
  14. Answer: 11111110₂ = 254₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 254₁₀

Foundations · Problem 0256

Read 11111111₂ 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: 11111111.
  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 1 at weight 128 contributes 128.
  5. Column 6: bit 1 at weight 64 contributes 64.
  6. Column 5: bit 1 at weight 32 contributes 32.
  7. Column 4: bit 1 at weight 16 contributes 16.
  8. Column 3: bit 1 at weight 8 contributes 8.
  9. Column 2: bit 1 at weight 4 contributes 4.
  10. Column 1: bit 1 at weight 2 contributes 2.
  11. Column 0: bit 1 at weight 1 contributes 1.
  12. The one-bit weights are 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1.
  13. Add just the selected weights: 255.
  14. Answer: 11111111₂ = 255₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 255₁₀