Binary to Decimal Conversion Practice Worksheet
Binary to decimal conversion exercise with a table showing binary numbers and their decimal equivalents, including a worked example.
JPG
622×713
91.5 KB
Free · Personal Use
Quality Assured by Worksheets Library Team
Reviewed for educational accuracy and age-appropriateness
ID: #741402
⭐
Show Answer Key & Explanations
Step-by-step solution for: Solved Exercise 1- Binary to Decimal Conversion Find the | Chegg.com
▼
Show Answer Key & Explanations
Step-by-step solution for: Solved Exercise 1- Binary to Decimal Conversion Find the | Chegg.com
Let's solve the Binary to Decimal Conversion exercise step by step.
We are given a table with binary numbers, and we need to convert each binary number to its decimal equivalent using the place values:
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|-----|----|----|----|---|---|---|---|
Each digit in the binary number corresponds to one of these powers of 2. If the digit is 1, we include that power of 2 in the sum. If it’s 0, we skip it.
---
Binary: `1 0 0 1 0 0 1 0`
Breakdown:
- 128 → 1 → include: 128
- 64 → 0 → skip
- 32 → 0 → skip
- 16 → 1 → include: 16
- 8 → 0 → skip
- 4 → 0 → skip
- 2 → 1 → include: 2
- 1 → 0 → skip
Sum: 128 + 16 + 2 = 146 ✔
Now let's do the rest:
---
- 128 → 0 → skip
- 64 → 1 → 64
- 32 → 0 → skip
- 16 → 0 → skip
- 8 → 1 → 8
- 4 → 1 → 4
- 2 → 0 → skip
- 1 → 1 → 1
Sum: 64 + 8 + 4 + 1 = 77
✔ Answer: 77
---
- 128 → 1 → 128
- 64 → 1 → 64
- 32 → 1 → 32
- 16 → 1 → 16
- 8 → 0 → skip
- 4 → 0 → skip
- 2 → 0 → skip
- 1 → 0 → skip
Sum: 128 + 64 + 32 + 16 = 240
✔ Answer: 240
---
- 128 → 0 → skip
- 64 → 1 → 64
- 32 → 1 → 32
- 16 → 0 → skip
- 8 → 0 → skip
- 4 → 1 → 4
- 2 → 1 → 2
- 1 → 1 → 1
Sum: 64 + 32 + 4 + 2 + 1 = 103
✔ Answer: 103
---
- 128 → 1 → 128
- 64 → 0 → skip
- 32 → 0 → skip
- 16 → 0 → skip
- 8 → 0 → skip
- 4 → 0 → skip
- 2 → 1 → 2
- 1 → 1 → 1
Sum: 128 + 2 + 1 = 131
✔ Answer: 131
---
- 128 → 1 → 128
- 64 → 1 → 64
- 32 → 1 → 32
- 16 → 1 → 16
- 8 → 1 → 8
- 4 → 1 → 4
- 2 → 0 → skip
- 1 → 1 → 1
Sum: 128 + 64 + 32 + 16 + 8 + 4 + 1 = 253
✔ Answer: 253
---
- 128 → 1 → 128
- 64 → 0 → skip
- 32 → 1 → 32
- 16 → 0 → skip
- 8 → 1 → 8
- 4 → 1 → 4
- 2 → 1 → 2
- 1 → 0 → skip
Sum: 128 + 32 + 8 + 4 + 2 = 174
✔ Answer: 174
---
- 128 → 1 → 128
- 64 → 0 → skip
- 32 → 0 → skip
- 16 → 1 → 16
- 8 → 1 → 8
- 4 → 1 → 4
- 2 → 0 → skip
- 1 → 0 → skip
Sum: 128 + 16 + 8 + 4 = 156
✔ Answer: 156
---
- 128 → 0 → skip
- 64 → 1 → 64
- 32 → 1 → 32
- 16 → 1 → 16
- 8 → 0 → skip
- 4 → 1 → 4
- 2 → 1 → 2
- 1 → 1 → 1
Sum: 64 + 32 + 16 + 4 + 2 + 1 = 119
✔ Answer: 119
---
- 128 → 1 → 128
- 64 → 0 → skip
- 32 → 0 → skip
- 16 → 1 → 16
- 8 → 0 → skip
- 4 → 1 → 4
- 2 → 0 → skip
- 1 → 0 → skip
Sum: 128 + 16 + 4 = 148
✔ Answer: 148
---
- 128 → 1 → 128
- 64 → 0 → skip
- 32 → 1 → 32
- 16 → 1 → 16
- 8 → 0 → skip
- 4 → 1 → 4
- 2 → 1 → 2
- 1 → 1 → 1
Sum: 128 + 32 + 16 + 4 + 2 + 1 = 183
✔ Answer: 183
---
- 128 → 0 → skip
- 64 → 1 → 64
- 32 → 0 → skip
- 16 → 0 → skip
- 8 → 0 → skip
- 4 → 0 → skip
- 2 → 1 → 2
- 1 → 0 → skip
Sum: 64 + 2 = 66
✔ Answer: 66
---
- 128 → 1 → 128
- 64 → 0 → skip
- 32 → 1 → 32
- 16 → 0 → skip
- 8 → 1 → 8
- 4 → 1 → 4
- 2 → 0 → skip
- 1 → 1 → 1
Sum: 128 + 32 + 8 + 4 + 1 = 173
✔ Answer: 173
---
- 128 → 0 → skip
- 64 → 1 → 64
- 32 → 0 → skip
- 16 → 1 → 16
- 8 → 1 → 8
- 4 → 0 → skip
- 2 → 1 → 2
- 1 → 1 → 1
Sum: 64 + 16 + 8 + 2 + 1 = 91
✔ Answer: 91
---
| Binary Number | Decimal Value |
|---------------|----------------|
| 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 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 |
---
✔ All converted! Let me know if you'd like this as a downloadable file or formatted for printing.
We are given a table with binary numbers, and we need to convert each binary number to its decimal equivalent using the place values:
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|-----|----|----|----|---|---|---|---|
Each digit in the binary number corresponds to one of these powers of 2. If the digit is 1, we include that power of 2 in the sum. If it’s 0, we skip it.
---
Example: First row (already done)
Binary: `1 0 0 1 0 0 1 0`
Breakdown:
- 128 → 1 → include: 128
- 64 → 0 → skip
- 32 → 0 → skip
- 16 → 1 → include: 16
- 8 → 0 → skip
- 4 → 0 → skip
- 2 → 1 → include: 2
- 1 → 0 → skip
Sum: 128 + 16 + 2 = 146 ✔
Now let's do the rest:
---
2. `0 1 0 0 1 1 0 1`
- 128 → 0 → skip
- 64 → 1 → 64
- 32 → 0 → skip
- 16 → 0 → skip
- 8 → 1 → 8
- 4 → 1 → 4
- 2 → 0 → skip
- 1 → 1 → 1
Sum: 64 + 8 + 4 + 1 = 77
✔ Answer: 77
---
3. `1 1 1 1 0 0 0 0`
- 128 → 1 → 128
- 64 → 1 → 64
- 32 → 1 → 32
- 16 → 1 → 16
- 8 → 0 → skip
- 4 → 0 → skip
- 2 → 0 → skip
- 1 → 0 → skip
Sum: 128 + 64 + 32 + 16 = 240
✔ Answer: 240
---
4. `0 1 1 0 0 1 1 1`
- 128 → 0 → skip
- 64 → 1 → 64
- 32 → 1 → 32
- 16 → 0 → skip
- 8 → 0 → skip
- 4 → 1 → 4
- 2 → 1 → 2
- 1 → 1 → 1
Sum: 64 + 32 + 4 + 2 + 1 = 103
✔ Answer: 103
---
5. `1 0 0 0 0 0 1 1`
- 128 → 1 → 128
- 64 → 0 → skip
- 32 → 0 → skip
- 16 → 0 → skip
- 8 → 0 → skip
- 4 → 0 → skip
- 2 → 1 → 2
- 1 → 1 → 1
Sum: 128 + 2 + 1 = 131
✔ Answer: 131
---
6. `1 1 1 1 1 1 0 1`
- 128 → 1 → 128
- 64 → 1 → 64
- 32 → 1 → 32
- 16 → 1 → 16
- 8 → 1 → 8
- 4 → 1 → 4
- 2 → 0 → skip
- 1 → 1 → 1
Sum: 128 + 64 + 32 + 16 + 8 + 4 + 1 = 253
✔ Answer: 253
---
7. `1 0 1 0 1 1 1 0`
- 128 → 1 → 128
- 64 → 0 → skip
- 32 → 1 → 32
- 16 → 0 → skip
- 8 → 1 → 8
- 4 → 1 → 4
- 2 → 1 → 2
- 1 → 0 → skip
Sum: 128 + 32 + 8 + 4 + 2 = 174
✔ Answer: 174
---
8. `1 0 0 1 1 1 0 0`
- 128 → 1 → 128
- 64 → 0 → skip
- 32 → 0 → skip
- 16 → 1 → 16
- 8 → 1 → 8
- 4 → 1 → 4
- 2 → 0 → skip
- 1 → 0 → skip
Sum: 128 + 16 + 8 + 4 = 156
✔ Answer: 156
---
9. `0 1 1 1 0 1 1 1`
- 128 → 0 → skip
- 64 → 1 → 64
- 32 → 1 → 32
- 16 → 1 → 16
- 8 → 0 → skip
- 4 → 1 → 4
- 2 → 1 → 2
- 1 → 1 → 1
Sum: 64 + 32 + 16 + 4 + 2 + 1 = 119
✔ Answer: 119
---
10. `1 0 0 1 0 1 0 0`
- 128 → 1 → 128
- 64 → 0 → skip
- 32 → 0 → skip
- 16 → 1 → 16
- 8 → 0 → skip
- 4 → 1 → 4
- 2 → 0 → skip
- 1 → 0 → skip
Sum: 128 + 16 + 4 = 148
✔ Answer: 148
---
11. `1 0 1 1 0 1 1 1`
- 128 → 1 → 128
- 64 → 0 → skip
- 32 → 1 → 32
- 16 → 1 → 16
- 8 → 0 → skip
- 4 → 1 → 4
- 2 → 1 → 2
- 1 → 1 → 1
Sum: 128 + 32 + 16 + 4 + 2 + 1 = 183
✔ Answer: 183
---
12. `0 1 0 0 0 0 1 0`
- 128 → 0 → skip
- 64 → 1 → 64
- 32 → 0 → skip
- 16 → 0 → skip
- 8 → 0 → skip
- 4 → 0 → skip
- 2 → 1 → 2
- 1 → 0 → skip
Sum: 64 + 2 = 66
✔ Answer: 66
---
13. `1 0 1 0 1 1 0 1`
- 128 → 1 → 128
- 64 → 0 → skip
- 32 → 1 → 32
- 16 → 0 → skip
- 8 → 1 → 8
- 4 → 1 → 4
- 2 → 0 → skip
- 1 → 1 → 1
Sum: 128 + 32 + 8 + 4 + 1 = 173
✔ Answer: 173
---
14. `0 1 0 1 1 0 1 1`
- 128 → 0 → skip
- 64 → 1 → 64
- 32 → 0 → skip
- 16 → 1 → 16
- 8 → 1 → 8
- 4 → 0 → skip
- 2 → 1 → 2
- 1 → 1 → 1
Sum: 64 + 16 + 8 + 2 + 1 = 91
✔ Answer: 91
---
Final Answers:
| Binary Number | Decimal Value |
|---------------|----------------|
| 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 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 |
---
✔ All converted! Let me know if you'd like this as a downloadable file or formatted for printing.
Parent Tip: Review the logic above to help your child master the concept of binary to decimal conversion worksheet.
