Explanation
1. Convert the Integer Part (56) to Binary
Divide by 2 repeatedly:
- 56 ÷ 2 = 28 remainder 0
- 28 ÷ 2 = 14 remainder 0
- 14 ÷ 2 = 7 remainder 0
- 7 ÷ 2 = 3 remainder 1
- 3 ÷ 2 = 1 remainder 1
- 1 ÷ 2 = 0 remainder 1
Now, write remainders bottom to top:
56₁₀ = 111000₂
2. Convert the Fractional Part (0.625) to Binary
Multiply by 2 repeatedly and take the integer part:
- 0.625 × 2 = 1.25 → 1
- 0.25 × 2 = 0.5 → 0
- 0.5 × 2 = 1.0 → 1
So, 0.625₁₀ = .101₂
Final Answer:
56.625₁₀ = 111000.101₂