The number 10101111 in binary system is represented in decimal system by which one of the following numbers?

Options

A. 157
B. 175
C. 571
D. 751

Answer

To convert the binary number 10101111 to its decimal equivalent, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the binary number**: The given binary number is 10101111.

2. **Write down the place values**: Each digit in a binary number represents a power of 2, starting from the rightmost digit (which is 2^0). The place values for the binary number 10101111 are as follows:
- 1 × 2^7
- 0 × 2^6
- 1 × 2^5
- 0 × 2^4
- 1 × 2^3
- 1 × 2^2
- 1 × 2^1
- 1 × 2^0

3. **Calculate the values**:
- 1 × 2^7 = 1 × 128 = 128
- 0 × 2^6 = 0 × 64 = 0
- 1 × 2^5 = 1 × 32 = 32
- 0 × 2^4 = 0 × 16 = 0
- 1 × 2^3 = 1 × 8 = 8
- 1 × 2^2 = 1 × 4 = 4
- 1 × 2^1 = 1 × 2 = 2
- 1 × 2^0 = 1 × 1 = 1

4. **Sum the values**: Now, we add all these calculated values together:
- 128 + 0 + 32 + 0 + 8 + 4 + 2 + 1 = 175

5. **Conclusion**: Therefore, the decimal representation of the binary number 10101111 is 175.

### Final Answer:
The number 10101111 in binary system is represented in decimal system by 175.

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