You're given a binary-to-decimal conversion exercise. Each row represents an 8-bit binary number, and the column headers (128, 64, 32, 16, 8, 4, 2, 1) are the
place values in binary (powers of 2 from 2⁷ down to 2⁰).
To convert binary to decimal:
>
Add up the place values where there’s a '1' in that position.
Let’s go row by row.
---
✔ First one is done:
`1 0 0 1 0 0 1 0` → 128 + 16 + 2 =
146
---
Row 2: `0 1 0 0 1 1 0 1`
Place values with 1s: 64, 8, 4, 1
→ 64 + 8 + 4 + 1 =
77
---
Row 3: `1 1 1 1 0 0 0 0`
Place values with 1s: 128, 64, 32, 16
→ 128 + 64 + 32 + 16 =
240
---
Row 4: `0 1 1 0 0 1 1 1`
Place values with 1s: 64, 32, 4, 2, 1
→ 64 + 32 + 4 + 2 + 1 =
103
---
Row 5: `1 0 0 0 0 0 1 1`
Place values with 1s: 128, 2, 1
→ 128 + 2 + 1 =
131
---
Row 6: `1 1 1 1 1 1 0 1`
Place values with 1s: 128, 64, 32, 16, 8, 4, 1
→ 128 + 64 + 32 + 16 + 8 + 4 + 1 =
253
---
Row 7: `1 0 1 0 1 1 1 0`
Place values with 1s: 128, 32, 8, 4, 2
→ 128 + 32 + 8 + 4 + 2 =
174
---
Row 8: `1 0 0 1 1 1 0 0`
Place values with 1s: 128, 16, 8, 4
→ 128 + 16 + 8 + 4 =
156
---
Row 9: `0 1 0 1 0 1 0 0`
Place values with 1s: 64, 16, 4
→ 64 + 16 + 4 =
84
---
Row 10: `0 1 1 1 0 1 1 1`
Place values with 1s: 64, 32, 16, 4, 2, 1
→ 64 + 32 + 16 + 4 + 2 + 1 =
119
---
Row 11: `1 0 0 1 0 1 0 0`
Place values with 1s: 128, 16, 4
→ 128 + 16 + 4 =
148
---
Row 12: `1 0 1 1 0 1 1 1`
Place values with 1s: 128, 32, 16, 4, 2, 1
→ 128 + 32 + 16 + 4 + 2 + 1 =
183
---
Row 13: `0 1 0 0 0 0 1 0`
Place values with 1s: 64, 2
→ 64 + 2 =
66
---
Row 14: `1 0 1 0 1 1 0 1`
Place values with 1s: 128, 32, 8, 4, 1
→ 128 + 32 + 8 + 4 + 1 =
173
---
Row 15: `0 1 0 1 1 0 1 1`
Place values with 1s: 64, 16, 8, 2, 1
→ 64 + 16 + 8 + 2 + 1 =
91
---
##
✔ Final Answers:
| Binary | Decimal |
|------------------|---------|
| 1 0 0 1 0 0 1 0 | 146 |
| 0 1 0 0 1 1 0 1 |
77 |
| 1 1 1 1 0 0 0 0 |
240 |
| 0 1 1 0 0 1 1 1 |
103 |
| 1 0 0 0 0 0 1 1 |
131 |
| 1 1 1 1 1 1 0 1 |
253 |
| 1 0 1 0 1 1 1 0 |
174 |
| 1 0 0 1 1 1 0 0 |
156 |
| 0 1 0 1 0 1 0 0 |
84 |
| 0 1 1 1 0 1 1 1 |
119 |
| 1 0 0 1 0 1 0 0 |
148 |
| 1 0 1 1 0 1 1 1 |
183 |
| 0 1 0 0 0 0 1 0 |
66 |
| 1 0 1 0 1 1 0 1 |
173 |
| 0 1 0 1 1 0 1 1 |
91 |
---
📌
Tip: You can also use this shortcut — write the binary number, then multiply each digit by its place value (from right to left: 1, 2, 4, 8, 16, 32, 64, 128), and sum only those with 1s.
Let me know if you want to check your scratch work or need help understanding any step!
Parent Tip: Review the logic above to help your child master the concept of binary to decimal worksheet.
