Convert `(1101.0101)_2` in base 10 (i.e., decimal system)

Answer

To convert the binary number `(1101.0101)_2` to decimal (base 10), we will follow these steps:

### Step 1: Identify the whole and fractional parts
The binary number `1101.0101` consists of two parts:
- Whole part: `1101`
- Fractional part: `0101`

### Step 2: Convert the whole part to decimal
To convert the whole part `1101` from binary to decimal, we will multiply each digit by 2 raised to the power of its position (counting from right to left, starting at 0).

- The binary digits from right to left are:
- 1 (at position 0)
- 0 (at position 1)
- 1 (at position 2)
- 1 (at position 3)

The calculation will be:
- \(1 \times 2^3 + 1 \times 2^2 + 0 \times 2^1 + 1 \times 2^0\)
- \(= 1 \times 8 + 1 \times 4 + 0 \times 2 + 1 \times 1\)
- \(= 8 + 4 + 0 + 1\)
- \(= 13\)

### Step 3: Convert the fractional part to decimal
To convert the fractional part `0101` from binary to decimal, we will multiply each digit by 2 raised to the power of its position (counting from left to right, starting at -1).

- The binary digits from left to right are:
- 0 (at position -1)
- 1 (at position -2)
- 0 (at position -3)
- 1 (at position -4)

The calculation will be:
- \(0 \times 2^{-1} + 1 \times 2^{-2} + 0 \times 2^{-3} + 1 \times 2^{-4}\)
- \(= 0 \times 0.5 + 1 \times 0.25 + 0 \times 0.125 + 1 \times 0.0625\)
- \(= 0 + 0.25 + 0 + 0.0625\)
- \(= 0.3125\)

### Step 4: Combine the whole and fractional parts
Now, we combine the results from the whole and fractional parts:
- Whole part: `13`
- Fractional part: `0.3125`

Thus, the final result is:
- \(13 + 0.3125 = 13.3125\)

### Final Answer
The decimal (base 10) equivalent of the binary number `(1101.0101)_2` is **13.3125**.

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