Solution

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