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Convert the Decimal Number 108.25 to Its Binary Equivalent

Convert the Decimal Number 108.25 to Its Binary Equivalent

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Nov 4, 2026

To convert 108.2510108.25_{10} to binary, split the number into its integer part and fractional part:

  • Integer part: 108108
  • Fractional part: 0.250.25

We convert each part separately using standard methods: Integer-to-binary and Fraction-to-binary. Then we concatenate the results around the binary point.

Below is the full conversion using the integer-part and fractional-part rules.

Convert the integer part: 108 to binary

  1. 1
    Step 1

    Divide 108 by 2 repeatedly, recording the remainders (these remainders become the binary digits from right to left).

  2. 2
    Step 2

    108 ÷ 2 = 54 remainder 0; 54 ÷ 2 = 27 remainder 0; 27 ÷ 2 = 13 remainder 1; 13 ÷ 2 = 6 remainder 1; 6 ÷ 2 = 3 remainder 0; 3 ÷ 2 = 1 remainder 1; 1 ÷ 2 = 0 remainder 1.

  3. 3
    Step 3

    Remainders from last to first: 1, 1, 0, 1, 1, 0, 0 → 10810=11011002108_{10} = 1101100_2.

  4. 4
    Step 4

    Integer part in binary is 110110021101100_2.

Convert the fractional part: 0.25 to binary

  1. 1
    Step 1

    Multiply the fractional part by 2 repeatedly; the integer parts of each product become the binary digits after the point.

  2. 2
    Step 2

    0.25 × 2 = 0.50 → integer digit 0; remaining fraction 0.50. Next: 0.50 × 2 = 1.00 → integer digit 1; remaining fraction 0.00.

  3. 3
    Step 3

    Once the fractional remainder is 0, no more digits are needed.

  4. 4
    Step 4

    Digits collected in order: 0 then 1 → 0.2510=0.0120.25_{10} = 0.01_2.

Now concatenate integer and fractional results around the binary point:

  • 10810=11011002108_{10} = 1101100_2
  • 0.2510=0.0120.25_{10} = 0.01_2

So:

108.2510=1101100.012108.25_{10} = 1101100.01_2

Pro Tip: fractions like 0.25 convert quickly

Because 0.25=14=2−20.25 = \frac{1}{4} = 2^{-2}, its binary form terminates after exactly 2 fractional bits: 0.0120.01_2.

Common mistake: mixing integer vs fractional conversion

Don’t use repeated multiplication for the whole number (e.g., 108). Integer conversion uses repeated division by 2; fractional conversion uses repeated multiplication by 2.

Conversion Workflow (108.25 → binary)

Split

1

Separate into 108108 and 0.250.25."

Integer conversion

2

Use division by 2 and collect remainders."

Fraction conversion

3

Use multiplication by 2 and collect integer parts."

Combine

4

Join results as integer bits.fraction bits\text{integer bits} . \text{fraction bits}."

Binary digit derivation (quick view)

Integer part uses remainders from division; fractional part uses integer parts from multiplication.

Quick Checks & Edge Cases

Knowledge Check

Question 1 of 4
Q1Single choice

What is the binary representation of the integer part 10810108_{10}?

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