Let's solve each binary number by converting it to denary (decimal). The method involves multiplying each binary digit (bit) by its corresponding power of 2 (from right to left, starting with \(2^0 = 1\)), and then summing the results.
The powers of 2 for an 8-bit binary number are:
```
128 64 32 16 8 4 2 1
```
We only add the values where the bit is
1.
---
1.
Binary: `0 0 0 0 0 0 1 1`
Only the last two bits are 1 → values: 2 and 1
→ \(2 + 1 = 3\)
✔ Answer: 3
---
2.
Binary: `0 0 0 0 0 1 0 1`
Bits at 4 and 1 are 1 → values: 4 and 1
→ \(4 + 1 = 5\)
✔ Answer: 5
---
3.
Binary: `0 0 0 1 0 1 0 0`
Bits at 16 and 4 are 1 → values: 16 and 4
→ \(16 + 4 = 20\)
✔ Answer: 20
---
4.
Binary: `1 0 0 1 0 1 0 0`
Bits at 128, 16, and 4 are 1 → values: 128, 16, 4
→ \(128 + 16 + 4 = 148\)
✔ Answer: 148
---
5.
Binary: `0 0 1 0 1 1 0 0`
Bits at 32, 8, and 4 are 1 → values: 32, 8, 4
→ \(32 + 8 + 4 = 44\)
✔ Answer: 44
---
6.
Binary: `0 1 0 1 0 1 0 1`
Bits at 64, 16, 4, and 1 are 1 → values: 64, 16, 4, 1
→ \(64 + 16 + 4 + 1 = 85\)
✔ Answer: 85
---
✔ Final Answers:
1.
3
2.
5
3.
20
4.
148
5.
44
6.
85
You can fill these into the boxes on the worksheet accordingly.
Parent Tip: Review the logic above to help your child master the concept of binary numbers worksheet.
