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

Explanation

To convert the binary number 10101111 into its decimal equivalent, we will follow these steps:

### Step 1: Write down the binary number and assign powers of 2
The binary number is 10101111. We will assign powers of 2 starting from the rightmost digit (which is 2^0) to the leftmost digit (which is 2^7).

```
Binary: 1 0 1 0 1 1 1 1
Powers: 2^7 2^6 2^5 2^4 2^3 2^2 2^1 2^0
```

### Step 2: Identify the values of each binary digit
Now we will multiply each binary digit by its corresponding power of 2:

- 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

### Step 3: Sum all the values
Now we will add all these values together:

```
128 + 0 + 32 + 0 + 8 + 4 + 2 + 1 = 175
```

### Conclusion
The decimal representation of the binary number 10101111 is **175**.

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