Worksheet for converting binary numbers to decimal values.

Let's solve the binary to decimal conversion problems step by step.

To convert a binary number to decimal, we use the positional values of each digit in the binary number. Each digit represents a power of 2, starting from the rightmost digit (which is $2^0$) and moving left.

For example:
- Binary: `1011`
- Decimal: $1 \times 2^3 + 0 \times 2^2 + 1 \times 2^1 + 1 \times 2^0 = 8 + 0 + 2 + 1 = 11$

We'll apply this method to all the given binary numbers.

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Solutions:

#### 1) `11010101`
- $1 \times 2^7 = 128$
- $1 \times 2^6 = 64$
- $0 \times 2^5 = 0$
- $1 \times 2^4 = 16$
- $0 \times 2^3 = 0$
- $1 \times 2^2 = 4$
- $0 \times 2^1 = 0$
- $1 \times 2^0 = 1$
- Total: $128 + 64 + 16 + 4 + 1 = 213$

✔ 213

---

#### 2) `10100000`
- $1 \times 2^7 = 128$
- $0 \times 2^6 = 0$
- $1 \times 2^5 = 32$
- $0 \times 2^4 = 0$
- $0 \times 2^3 = 0$
- $0 \times 2^2 = 0$
- $0 \times 2^1 = 0$
- $0 \times 2^0 = 0$
- Total: $128 + 32 = 160$

✔ 160

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#### 3) `11000111`
- $1 \times 2^7 = 128$
- $1 \times 2^6 = 64$
- $0 \times 2^5 = 0$
- $0 \times 2^4 = 0$
- $0 \times 2^3 = 0$
- $1 \times 2^2 = 4$
- $1 \times 2^1 = 2$
- $1 \times 2^0 = 1$
- Total: $128 + 64 + 4 + 2 + 1 = 200$

✔ 200

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#### 4) `10100111`
- $1 \times 2^7 = 128$
- $0 \times 2^6 = 0$
- $1 \times 2^5 = 32$
- $0 \times 2^4 = 0$
- $0 \times 2^3 = 0$
- $1 \times 2^2 = 4$
- $1 \times 2^1 = 2$
- $1 \times 2^0 = 1$
- Total: $128 + 32 + 4 + 2 + 1 = 167$

✔ 167

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#### 5) `11011111`
- $1 \times 2^7 = 128$
- $1 \times 2^6 = 64$
- $0 \times 2^5 = 0$
- $1 \times 2^4 = 16$
- $1 \times 2^3 = 8$
- $1 \times 2^2 = 4$
- $1 \times 2^1 = 2$
- $1 \times 2^0 = 1$
- Total: $128 + 64 + 16 + 8 + 4 + 2 + 1 = 223$

✔ 223

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#### 6) `10111101`
- $1 \times 2^7 = 128$
- $0 \times 2^6 = 0$
- $1 \times 2^5 = 32$
- $1 \times 2^4 = 16$
- $1 \times 2^3 = 8$
- $1 \times 2^2 = 4$
- $0 \times 2^1 = 0$
- $1 \times 2^0 = 1$
- Total: $128 + 32 + 16 + 8 + 4 + 1 = 189$

✔ 189

---

#### 7) `01110000`
- Leading zero doesn't affect value.
- $0 \times 2^7 = 0$
- $1 \times 2^6 = 64$
- $1 \times 2^5 = 32$
- $1 \times 2^4 = 16$
- $0 \times 2^3 = 0$
- $0 \times 2^2 = 0$
- $0 \times 2^1 = 0$
- $0 \times 2^0 = 0$
- Total: $64 + 32 + 16 = 112$

✔ 112

---

#### 8) `10001110`
- $1 \times 2^7 = 128$
- $0 \times 2^6 = 0$
- $0 \times 2^5 = 0$
- $0 \times 2^4 = 0$
- $1 \times 2^3 = 8$
- $1 \times 2^2 = 4$
- $1 \times 2^1 = 2$
- $0 \times 2^0 = 0$
- Total: $128 + 8 + 4 + 2 = 142$

✔ 142

---

#### 9) `01101110`
- $0 \times 2^7 = 0$
- $1 \times 2^6 = 64$
- $1 \times 2^5 = 32$
- $0 \times 2^4 = 0$
- $1 \times 2^3 = 8$
- $1 \times 2^2 = 4$
- $1 \times 2^1 = 2$
- $0 \times 2^0 = 0$
- Total: $64 + 32 + 8 + 4 + 2 = 106$

✔ 106

---

#### 10) `11110000`
- $1 \times 2^7 = 128$
- $1 \times 2^6 = 64$
- $1 \times 2^5 = 32$
- $1 \times 2^4 = 16$
- $0 \times 2^3 = 0$
- $0 \times 2^2 = 0$
- $0 \times 2^1 = 0$
- $0 \times 2^0 = 0$
- Total: $128 + 64 + 32 + 16 = 240$

✔ 240

---

#### 11) `11001000`
- $1 \times 2^7 = 128$
- $1 \times 2^6 = 64$
- $0 \times 2^5 = 0$
- $0 \times 2^4 = 0$
- $1 \times 2^3 = 8$
- $0 \times 2^2 = 0$
- $0 \times 2^1 = 0$
- $0 \times 2^0 = 0$
- Total: $128 + 64 + 8 = 200$

✔ 200

---

#### 12) `10000011`
- $1 \times 2^7 = 128$
- $0 \times 2^6 = 0$
- $0 \times 2^5 = 0$
- $0 \times 2^4 = 0$
- $0 \times 2^3 = 0$
- $0 \times 2^2 = 0$
- $1 \times 2^1 = 2$
- $1 \times 2^0 = 1$
- Total: $128 + 2 + 1 = 131$

✔ 131

---

#### 13) `00000001`
- Only last digit is 1 → $1 \times 2^0 = 1$

✔ 1

---

#### 14) `10000010`
- $1 \times 2^7 = 128$
- $0 \times 2^6 = 0$
- $0 \times 2^5 = 0$
- $0 \times 2^4 = 0$
- $0 \times 2^3 = 0$
- $0 \times 2^2 = 0$
- $1 \times 2^1 = 2$
- $0 \times 2^0 = 0$
- Total: $128 + 2 = 130$

✔ 130

---

#### 15) `11101110`
- $1 \times 2^7 = 128$
- $1 \times 2^6 = 64$
- $1 \times 2^5 = 32$
- $0 \times 2^4 = 0$
- $1 \times 2^3 = 8$
- $1 \times 2^2 = 4$
- $1 \times 2^1 = 2$
- $0 \times 2^0 = 0$
- Total: $128 + 64 + 32 + 8 + 4 + 2 = 238$

✔ 238

---

#### 16) `10101010`
- $1 \times 2^7 = 128$
- $0 \times 2^6 = 0$
- $1 \times 2^5 = 32$
- $0 \times 2^4 = 0$
- $1 \times 2^3 = 8$
- $0 \times 2^2 = 0$
- $1 \times 2^1 = 2$
- $0 \times 2^0 = 0$
- Total: $128 + 32 + 8 + 2 = 170$

✔ 170

---

#### 17) `01100001`
- $0 \times 2^7 = 0$
- $1 \times 2^6 = 64$
- $1 \times 2^5 = 32$
- $0 \times 2^4 = 0$
- $0 \times 2^3 = 0$
- $0 \times 2^2 = 0$
- $0 \times 2^1 = 0$
- $1 \times 2^0 = 1$
- Total: $64 + 32 + 1 = 97$

✔ 97

---

#### 18) `00011100`
- $0 \times 2^7 = 0$
- $0 \times 2^6 = 0$
- $0 \times 2^5 = 0$
- $1 \times 2^4 = 16$
- $1 \times 2^3 = 8$
- $1 \times 2^2 = 4$
- $0 \times 2^1 = 0$
- $0 \times 2^0 = 0$
- Total: $16 + 8 + 4 = 28$

✔ 28

---

#### 19) `00110001`
- $0 \times 2^7 = 0$
- $0 \times 2^6 = 0$
- $1 \times 2^5 = 32$
- $1 \times 2^4 = 16$
- $0 \times 2^3 = 0$
- $0 \times 2^2 = 0$
- $0 \times 2^1 = 0$
- $1 \times 2^0 = 1$
- Total: $32 + 16 + 1 = 49$

✔ 49

---

#### 20) `11100011`
- $1 \times 2^7 = 128$
- $1 \times 2^6 = 64$
- $1 \times 2^5 = 32$
- $0 \times 2^4 = 0$
- $0 \times 2^3 = 0$
- $0 \times 2^2 = 0$
- $1 \times 2^1 = 2$
- $1 \times 2^0 = 1$
- Total: $128 + 64 + 32 + 2 + 1 = 227$

✔ 227

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#### 21) `11011000`
- $1 \times 2^7 = 128$
- $1 \times 2^6 = 64$
- $0 \times 2^5 = 0$
- $1 \times 2^4 = 16$
- $1 \times 2^3 = 8$
- $0 \times 2^2 = 0$
- $0 \times 2^1 = 0$
- $0 \times 2^0 = 0$
- Total: $128 + 64 + 16 + 8 = 216$

✔ 216

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#### 22) `10010000`
- $1 \times 2^7 = 128$
- $0 \times 2^6 = 0$
- $0 \times 2^5 = 0$
- $1 \times 2^4 = 16$
- $0 \times 2^3 = 0$
- $0 \times 2^2 = 0$
- $0 \times 2^1 = 0$
- $0 \times 2^0 = 0$
- Total: $128 + 16 = 144$

✔ 144

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#### 23) `01010100`
- $0 \times 2^7 = 0$
- $1 \times 2^6 = 64$
- $0 \times 2^5 = 0$
- $1 \times 2^4 = 16$
- $0 \times 2^3 = 0$
- $1 \times 2^2 = 4$
- $0 \times 2^1 = 0$
- $0 \times 2^0 = 0$
- Total: $64 + 16 + 4 = 84$

✔ 84

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#### 24) `11101011`
- $1 \times 2^7 = 128$
- $1 \times 2^6 = 64$
- $1 \times 2^5 = 32$
- $0 \times 2^4 = 0$
- $1 \times 2^3 = 8$
- $0 \times 2^2 = 0$
- $1 \times 2^1 = 2$
- $1 \times 2^0 = 1$
- Total: $128 + 64 + 32 + 8 + 2 + 1 = 235$

✔ 235

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✔ Final Answers:

| No. | Binary | Decimal |
|-----|---------------|---------|
| 1 | 11010101 | 213 |
| 2 | 10100000 | 160 |
| 3 | 11000111 | 200 |
| 4 | 10100111 | 167 |
| 5 | 11011111 | 223 |
| 6 | 10111101 | 189 |
| 7 | 01110000 | 112 |
| 8 | 10001110 | 142 |
| 9 | 01101110 | 106 |
|10 | 11110000 | 240 |
|11 | 11001000 | 200 |
|12 | 10000011 | 131 |
|13 | 00000001 | 1 |
|14 | 10000010 | 130 |
|15 | 11101110 | 238 |
|16 | 10101010 | 170 |
|17 | 01100001 | 97 |
|18 | 00011100 | 28 |
|19 | 00110001 | 49 |
|20 | 11100011 | 227 |
|21 | 11011000 | 216 |
|22 | 10010000 | 144 |
|23 | 01010100 | 84 |
|24 | 11101011 | 235 |

Let me know if you'd like these explained in a table format or need help with decimal-to-binary conversions too!