Question

convert the following real numbers to binary (five binary places)  a.34.10

Answer 1

To convert the decimal number 34.10 into binary (with five binary places), we can break it down into two parts: the integer part (34) and the fractional part (0.10).

### Step 1: Convert the integer part (34) to binary.

1. Divide the number by 2 and keep track of the remainders:
- \(34 \div 2 = 17\) remainder \(0\)
- \(17 \div 2 = 8\) remainder \(1\)
- \(8 \div 2 = 4\) remainder \(0\)
- \(4 \div 2 = 2\) remainder \(0\)
- \(2 \div 2 = 1\) remainder \(0\)
- \(1 \div 2 = 0\) remainder \(1\)

2. Read the remainders from bottom to top:
- \(34_{10} = 100010_{2}\)

### Step 2: Convert the fractional part (0.10) to binary.

To convert the fractional part (0.10), we multiply it by 2 and keep track of the integer parts:

1. \(0.10 \times 2 = 0.20\) → integer part: \(0\)
2. \(0.20 \times 2 = 0.40\) → integer part: \(0\)
3. \(0.40 \times 2 = 0.80\) → integer part: \(0\)
4. \(0.80 \times 2 = 1.60\) → integer part: \(1\)
5. \(0.60 \times 2 = 1.20\) → integer part: \(1\)

After five iterations, the integer parts give us: \(00011\).

### Step 3: Combine the integer and fractional parts.

Now, we can combine both parts:
- Integer part: 100010
- Fractional part: .00011

So, the full binary representation of \(34.10_{10}\) in binary (with five binary places after the decimal) is:

**100010.00011**