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Reading binary

Set 7 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 0193

Read 11000000₂ 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: 11000000.
  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 0 at weight 32 contributes 0.
  7. Column 4: bit 0 at weight 16 contributes 0.
  8. Column 3: bit 0 at weight 8 contributes 0.
  9. Column 2: bit 0 at weight 4 contributes 0.
  10. Column 1: bit 0 at weight 2 contributes 0.
  11. Column 0: bit 0 at weight 1 contributes 0.
  12. The one-bit weights are 128 + 64.
  13. Add just the selected weights: 192.
  14. Answer: 11000000₂ = 192₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 192₁₀

Foundations · Problem 0194

Read 11000001₂ 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: 11000001.
  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 0 at weight 32 contributes 0.
  7. Column 4: bit 0 at weight 16 contributes 0.
  8. Column 3: bit 0 at weight 8 contributes 0.
  9. Column 2: bit 0 at weight 4 contributes 0.
  10. Column 1: bit 0 at weight 2 contributes 0.
  11. Column 0: bit 1 at weight 1 contributes 1.
  12. The one-bit weights are 128 + 64 + 1.
  13. Add just the selected weights: 193.
  14. Answer: 11000001₂ = 193₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 193₁₀

Foundations · Problem 0195

Read 11000010₂ 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: 11000010.
  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 0 at weight 32 contributes 0.
  7. Column 4: bit 0 at weight 16 contributes 0.
  8. Column 3: bit 0 at weight 8 contributes 0.
  9. Column 2: bit 0 at weight 4 contributes 0.
  10. Column 1: bit 1 at weight 2 contributes 2.
  11. Column 0: bit 0 at weight 1 contributes 0.
  12. The one-bit weights are 128 + 64 + 2.
  13. Add just the selected weights: 194.
  14. Answer: 11000010₂ = 194₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 194₁₀

Foundations · Problem 0196

Read 11000011₂ 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: 11000011.
  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 0 at weight 32 contributes 0.
  7. Column 4: bit 0 at weight 16 contributes 0.
  8. Column 3: bit 0 at weight 8 contributes 0.
  9. Column 2: bit 0 at weight 4 contributes 0.
  10. Column 1: bit 1 at weight 2 contributes 2.
  11. Column 0: bit 1 at weight 1 contributes 1.
  12. The one-bit weights are 128 + 64 + 2 + 1.
  13. Add just the selected weights: 195.
  14. Answer: 11000011₂ = 195₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 195₁₀

Foundations · Problem 0197

Read 11000100₂ 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: 11000100.
  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 0 at weight 32 contributes 0.
  7. Column 4: bit 0 at weight 16 contributes 0.
  8. Column 3: bit 0 at weight 8 contributes 0.
  9. Column 2: bit 1 at weight 4 contributes 4.
  10. Column 1: bit 0 at weight 2 contributes 0.
  11. Column 0: bit 0 at weight 1 contributes 0.
  12. The one-bit weights are 128 + 64 + 4.
  13. Add just the selected weights: 196.
  14. Answer: 11000100₂ = 196₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 196₁₀

Foundations · Problem 0198

Read 11000101₂ 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: 11000101.
  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 0 at weight 32 contributes 0.
  7. Column 4: bit 0 at weight 16 contributes 0.
  8. Column 3: bit 0 at weight 8 contributes 0.
  9. Column 2: bit 1 at weight 4 contributes 4.
  10. Column 1: bit 0 at weight 2 contributes 0.
  11. Column 0: bit 1 at weight 1 contributes 1.
  12. The one-bit weights are 128 + 64 + 4 + 1.
  13. Add just the selected weights: 197.
  14. Answer: 11000101₂ = 197₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 197₁₀

Foundations · Problem 0199

Read 11000110₂ 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: 11000110.
  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 0 at weight 32 contributes 0.
  7. Column 4: bit 0 at weight 16 contributes 0.
  8. Column 3: bit 0 at weight 8 contributes 0.
  9. Column 2: bit 1 at weight 4 contributes 4.
  10. Column 1: bit 1 at weight 2 contributes 2.
  11. Column 0: bit 0 at weight 1 contributes 0.
  12. The one-bit weights are 128 + 64 + 4 + 2.
  13. Add just the selected weights: 198.
  14. Answer: 11000110₂ = 198₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 198₁₀

Foundations · Problem 0200

Read 11000111₂ 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: 11000111.
  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 0 at weight 32 contributes 0.
  7. Column 4: bit 0 at weight 16 contributes 0.
  8. Column 3: bit 0 at weight 8 contributes 0.
  9. Column 2: bit 1 at weight 4 contributes 4.
  10. Column 1: bit 1 at weight 2 contributes 2.
  11. Column 0: bit 1 at weight 1 contributes 1.
  12. The one-bit weights are 128 + 64 + 4 + 2 + 1.
  13. Add just the selected weights: 199.
  14. Answer: 11000111₂ = 199₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 199₁₀

Foundations · Problem 0201

Read 11001000₂ 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: 11001000.
  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 0 at weight 32 contributes 0.
  7. Column 4: bit 0 at weight 16 contributes 0.
  8. Column 3: bit 1 at weight 8 contributes 8.
  9. Column 2: bit 0 at weight 4 contributes 0.
  10. Column 1: bit 0 at weight 2 contributes 0.
  11. Column 0: bit 0 at weight 1 contributes 0.
  12. The one-bit weights are 128 + 64 + 8.
  13. Add just the selected weights: 200.
  14. Answer: 11001000₂ = 200₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 200₁₀

Foundations · Problem 0202

Read 11001001₂ 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: 11001001.
  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 0 at weight 32 contributes 0.
  7. Column 4: bit 0 at weight 16 contributes 0.
  8. Column 3: bit 1 at weight 8 contributes 8.
  9. Column 2: bit 0 at weight 4 contributes 0.
  10. Column 1: bit 0 at weight 2 contributes 0.
  11. Column 0: bit 1 at weight 1 contributes 1.
  12. The one-bit weights are 128 + 64 + 8 + 1.
  13. Add just the selected weights: 201.
  14. Answer: 11001001₂ = 201₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 201₁₀

Foundations · Problem 0203

Read 11001010₂ 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: 11001010.
  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 0 at weight 32 contributes 0.
  7. Column 4: bit 0 at weight 16 contributes 0.
  8. Column 3: bit 1 at weight 8 contributes 8.
  9. Column 2: bit 0 at weight 4 contributes 0.
  10. Column 1: bit 1 at weight 2 contributes 2.
  11. Column 0: bit 0 at weight 1 contributes 0.
  12. The one-bit weights are 128 + 64 + 8 + 2.
  13. Add just the selected weights: 202.
  14. Answer: 11001010₂ = 202₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 202₁₀

Foundations · Problem 0204

Read 11001011₂ 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: 11001011.
  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 0 at weight 32 contributes 0.
  7. Column 4: bit 0 at weight 16 contributes 0.
  8. Column 3: bit 1 at weight 8 contributes 8.
  9. Column 2: bit 0 at weight 4 contributes 0.
  10. Column 1: bit 1 at weight 2 contributes 2.
  11. Column 0: bit 1 at weight 1 contributes 1.
  12. The one-bit weights are 128 + 64 + 8 + 2 + 1.
  13. Add just the selected weights: 203.
  14. Answer: 11001011₂ = 203₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 203₁₀

Foundations · Problem 0205

Read 11001100₂ 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: 11001100.
  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 0 at weight 32 contributes 0.
  7. Column 4: bit 0 at weight 16 contributes 0.
  8. Column 3: bit 1 at weight 8 contributes 8.
  9. Column 2: bit 1 at weight 4 contributes 4.
  10. Column 1: bit 0 at weight 2 contributes 0.
  11. Column 0: bit 0 at weight 1 contributes 0.
  12. The one-bit weights are 128 + 64 + 8 + 4.
  13. Add just the selected weights: 204.
  14. Answer: 11001100₂ = 204₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 204₁₀

Foundations · Problem 0206

Read 11001101₂ 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: 11001101.
  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 0 at weight 32 contributes 0.
  7. Column 4: bit 0 at weight 16 contributes 0.
  8. Column 3: bit 1 at weight 8 contributes 8.
  9. Column 2: bit 1 at weight 4 contributes 4.
  10. Column 1: bit 0 at weight 2 contributes 0.
  11. Column 0: bit 1 at weight 1 contributes 1.
  12. The one-bit weights are 128 + 64 + 8 + 4 + 1.
  13. Add just the selected weights: 205.
  14. Answer: 11001101₂ = 205₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 205₁₀

Foundations · Problem 0207

Read 11001110₂ 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: 11001110.
  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 0 at weight 32 contributes 0.
  7. Column 4: bit 0 at weight 16 contributes 0.
  8. Column 3: bit 1 at weight 8 contributes 8.
  9. Column 2: bit 1 at weight 4 contributes 4.
  10. Column 1: bit 1 at weight 2 contributes 2.
  11. Column 0: bit 0 at weight 1 contributes 0.
  12. The one-bit weights are 128 + 64 + 8 + 4 + 2.
  13. Add just the selected weights: 206.
  14. Answer: 11001110₂ = 206₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 206₁₀

Foundations · Problem 0208

Read 11001111₂ 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: 11001111.
  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 0 at weight 32 contributes 0.
  7. Column 4: bit 0 at weight 16 contributes 0.
  8. Column 3: bit 1 at weight 8 contributes 8.
  9. Column 2: bit 1 at weight 4 contributes 4.
  10. Column 1: bit 1 at weight 2 contributes 2.
  11. Column 0: bit 1 at weight 1 contributes 1.
  12. The one-bit weights are 128 + 64 + 8 + 4 + 2 + 1.
  13. Add just the selected weights: 207.
  14. Answer: 11001111₂ = 207₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 207₁₀

Foundations · Problem 0209

Read 11010000₂ 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: 11010000.
  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 0 at weight 32 contributes 0.
  7. Column 4: bit 1 at weight 16 contributes 16.
  8. Column 3: bit 0 at weight 8 contributes 0.
  9. Column 2: bit 0 at weight 4 contributes 0.
  10. Column 1: bit 0 at weight 2 contributes 0.
  11. Column 0: bit 0 at weight 1 contributes 0.
  12. The one-bit weights are 128 + 64 + 16.
  13. Add just the selected weights: 208.
  14. Answer: 11010000₂ = 208₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 208₁₀

Foundations · Problem 0210

Read 11010001₂ 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: 11010001.
  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 0 at weight 32 contributes 0.
  7. Column 4: bit 1 at weight 16 contributes 16.
  8. Column 3: bit 0 at weight 8 contributes 0.
  9. Column 2: bit 0 at weight 4 contributes 0.
  10. Column 1: bit 0 at weight 2 contributes 0.
  11. Column 0: bit 1 at weight 1 contributes 1.
  12. The one-bit weights are 128 + 64 + 16 + 1.
  13. Add just the selected weights: 209.
  14. Answer: 11010001₂ = 209₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 209₁₀

Foundations · Problem 0211

Read 11010010₂ 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: 11010010.
  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 0 at weight 32 contributes 0.
  7. Column 4: bit 1 at weight 16 contributes 16.
  8. Column 3: bit 0 at weight 8 contributes 0.
  9. Column 2: bit 0 at weight 4 contributes 0.
  10. Column 1: bit 1 at weight 2 contributes 2.
  11. Column 0: bit 0 at weight 1 contributes 0.
  12. The one-bit weights are 128 + 64 + 16 + 2.
  13. Add just the selected weights: 210.
  14. Answer: 11010010₂ = 210₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 210₁₀

Foundations · Problem 0212

Read 11010011₂ 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: 11010011.
  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 0 at weight 32 contributes 0.
  7. Column 4: bit 1 at weight 16 contributes 16.
  8. Column 3: bit 0 at weight 8 contributes 0.
  9. Column 2: bit 0 at weight 4 contributes 0.
  10. Column 1: bit 1 at weight 2 contributes 2.
  11. Column 0: bit 1 at weight 1 contributes 1.
  12. The one-bit weights are 128 + 64 + 16 + 2 + 1.
  13. Add just the selected weights: 211.
  14. Answer: 11010011₂ = 211₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 211₁₀

Foundations · Problem 0213

Read 11010100₂ 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: 11010100.
  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 0 at weight 32 contributes 0.
  7. Column 4: bit 1 at weight 16 contributes 16.
  8. Column 3: bit 0 at weight 8 contributes 0.
  9. Column 2: bit 1 at weight 4 contributes 4.
  10. Column 1: bit 0 at weight 2 contributes 0.
  11. Column 0: bit 0 at weight 1 contributes 0.
  12. The one-bit weights are 128 + 64 + 16 + 4.
  13. Add just the selected weights: 212.
  14. Answer: 11010100₂ = 212₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 212₁₀

Foundations · Problem 0214

Read 11010101₂ 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: 11010101.
  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 0 at weight 32 contributes 0.
  7. Column 4: bit 1 at weight 16 contributes 16.
  8. Column 3: bit 0 at weight 8 contributes 0.
  9. Column 2: bit 1 at weight 4 contributes 4.
  10. Column 1: bit 0 at weight 2 contributes 0.
  11. Column 0: bit 1 at weight 1 contributes 1.
  12. The one-bit weights are 128 + 64 + 16 + 4 + 1.
  13. Add just the selected weights: 213.
  14. Answer: 11010101₂ = 213₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 213₁₀

Foundations · Problem 0215

Read 11010110₂ 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: 11010110.
  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 0 at weight 32 contributes 0.
  7. Column 4: bit 1 at weight 16 contributes 16.
  8. Column 3: bit 0 at weight 8 contributes 0.
  9. Column 2: bit 1 at weight 4 contributes 4.
  10. Column 1: bit 1 at weight 2 contributes 2.
  11. Column 0: bit 0 at weight 1 contributes 0.
  12. The one-bit weights are 128 + 64 + 16 + 4 + 2.
  13. Add just the selected weights: 214.
  14. Answer: 11010110₂ = 214₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 214₁₀

Foundations · Problem 0216

Read 11010111₂ 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: 11010111.
  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 0 at weight 32 contributes 0.
  7. Column 4: bit 1 at weight 16 contributes 16.
  8. Column 3: bit 0 at weight 8 contributes 0.
  9. Column 2: bit 1 at weight 4 contributes 4.
  10. Column 1: bit 1 at weight 2 contributes 2.
  11. Column 0: bit 1 at weight 1 contributes 1.
  12. The one-bit weights are 128 + 64 + 16 + 4 + 2 + 1.
  13. Add just the selected weights: 215.
  14. Answer: 11010111₂ = 215₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 215₁₀

Foundations · Problem 0217

Read 11011000₂ 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: 11011000.
  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 0 at weight 32 contributes 0.
  7. Column 4: bit 1 at weight 16 contributes 16.
  8. Column 3: bit 1 at weight 8 contributes 8.
  9. Column 2: bit 0 at weight 4 contributes 0.
  10. Column 1: bit 0 at weight 2 contributes 0.
  11. Column 0: bit 0 at weight 1 contributes 0.
  12. The one-bit weights are 128 + 64 + 16 + 8.
  13. Add just the selected weights: 216.
  14. Answer: 11011000₂ = 216₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 216₁₀

Foundations · Problem 0218

Read 11011001₂ 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: 11011001.
  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 0 at weight 32 contributes 0.
  7. Column 4: bit 1 at weight 16 contributes 16.
  8. Column 3: bit 1 at weight 8 contributes 8.
  9. Column 2: bit 0 at weight 4 contributes 0.
  10. Column 1: bit 0 at weight 2 contributes 0.
  11. Column 0: bit 1 at weight 1 contributes 1.
  12. The one-bit weights are 128 + 64 + 16 + 8 + 1.
  13. Add just the selected weights: 217.
  14. Answer: 11011001₂ = 217₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 217₁₀

Foundations · Problem 0219

Read 11011010₂ 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: 11011010.
  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 0 at weight 32 contributes 0.
  7. Column 4: bit 1 at weight 16 contributes 16.
  8. Column 3: bit 1 at weight 8 contributes 8.
  9. Column 2: bit 0 at weight 4 contributes 0.
  10. Column 1: bit 1 at weight 2 contributes 2.
  11. Column 0: bit 0 at weight 1 contributes 0.
  12. The one-bit weights are 128 + 64 + 16 + 8 + 2.
  13. Add just the selected weights: 218.
  14. Answer: 11011010₂ = 218₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 218₁₀

Foundations · Problem 0220

Read 11011011₂ 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: 11011011.
  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 0 at weight 32 contributes 0.
  7. Column 4: bit 1 at weight 16 contributes 16.
  8. Column 3: bit 1 at weight 8 contributes 8.
  9. Column 2: bit 0 at weight 4 contributes 0.
  10. Column 1: bit 1 at weight 2 contributes 2.
  11. Column 0: bit 1 at weight 1 contributes 1.
  12. The one-bit weights are 128 + 64 + 16 + 8 + 2 + 1.
  13. Add just the selected weights: 219.
  14. Answer: 11011011₂ = 219₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 219₁₀

Foundations · Problem 0221

Read 11011100₂ 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: 11011100.
  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 0 at weight 32 contributes 0.
  7. Column 4: bit 1 at weight 16 contributes 16.
  8. Column 3: bit 1 at weight 8 contributes 8.
  9. Column 2: bit 1 at weight 4 contributes 4.
  10. Column 1: bit 0 at weight 2 contributes 0.
  11. Column 0: bit 0 at weight 1 contributes 0.
  12. The one-bit weights are 128 + 64 + 16 + 8 + 4.
  13. Add just the selected weights: 220.
  14. Answer: 11011100₂ = 220₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 220₁₀

Foundations · Problem 0222

Read 11011101₂ 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: 11011101.
  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 0 at weight 32 contributes 0.
  7. Column 4: bit 1 at weight 16 contributes 16.
  8. Column 3: bit 1 at weight 8 contributes 8.
  9. Column 2: bit 1 at weight 4 contributes 4.
  10. Column 1: bit 0 at weight 2 contributes 0.
  11. Column 0: bit 1 at weight 1 contributes 1.
  12. The one-bit weights are 128 + 64 + 16 + 8 + 4 + 1.
  13. Add just the selected weights: 221.
  14. Answer: 11011101₂ = 221₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 221₁₀

Foundations · Problem 0223

Read 11011110₂ 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: 11011110.
  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 0 at weight 32 contributes 0.
  7. Column 4: bit 1 at weight 16 contributes 16.
  8. Column 3: bit 1 at weight 8 contributes 8.
  9. Column 2: bit 1 at weight 4 contributes 4.
  10. Column 1: bit 1 at weight 2 contributes 2.
  11. Column 0: bit 0 at weight 1 contributes 0.
  12. The one-bit weights are 128 + 64 + 16 + 8 + 4 + 2.
  13. Add just the selected weights: 222.
  14. Answer: 11011110₂ = 222₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 222₁₀

Foundations · Problem 0224

Read 11011111₂ 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: 11011111.
  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 0 at weight 32 contributes 0.
  7. Column 4: bit 1 at weight 16 contributes 16.
  8. Column 3: bit 1 at weight 8 contributes 8.
  9. Column 2: bit 1 at weight 4 contributes 4.
  10. Column 1: bit 1 at weight 2 contributes 2.
  11. Column 0: bit 1 at weight 1 contributes 1.
  12. The one-bit weights are 128 + 64 + 16 + 8 + 4 + 2 + 1.
  13. Add just the selected weights: 223.
  14. Answer: 11011111₂ = 223₁₀.
  15. Sanity check: the answer must lie between zero and the maximum unsigned value for this width.

Final answer: 223₁₀