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NIMCET 2023

Equivalent of the decimal number (25.375)10 in  binary form

Solution

Decimal to Binary Conversion

? Given: Convert (25.375)10 to binary.

? Step-by-step:

  • Integer Part (25):
    Divide by 2 repeatedly: 
    25 ÷ 2 = 12 remainder 1  
12 ÷ 2 = 6  remainder 0  
6  ÷ 2 = 3  remainder 0  
3  ÷ 2 = 1  remainder 1  
1  ÷ 2 = 0  remainder 1
    → Binary: 11001
  • Fractional Part (0.375):
    Multiply by 2 repeatedly: 
    0.375 × 2 = 0.75   → 0  
0.75 × 2  = 1.5    → 1  
0.5 × 2   = 1.0    → 1
    → Binary: .011

✅ Final Binary Answer: (25.375)10 = (11001.011)2

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