Convert (0.75)10 into binary.
(0.11)2
Converting Decimal 0.75 to Binary
This guide explains how to convert a decimal fraction, specifically 0.75, into its equivalent binary representation.
Understanding Decimal to Binary Conversion for Fractions
To convert the fractional part of a decimal number to binary, we use a method of repeated multiplication by 2. Here's how it works:
- Multiply the fractional part by 2.
- The integer part of the result is the next binary digit (bit).
- Use the fractional part of the result for the next multiplication.
- Repeat this process until the fractional part becomes 0 or you reach the desired precision.
- The binary digits are collected from the integer parts obtained in order.
Step-by-Step Conversion of (0.75)10
Let's apply this method to convert the decimal number 0.75 to binary:
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Start with the fractional part: 0.75.
Multiply by 2:
$0.75 \times 2 = 1.50$The integer part is 1. This is the first binary digit after the binary point.
The new fractional part is 0.50.
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Take the new fractional part: 0.50.
Multiply by 2:
$0.50 \times 2 = 1.00$The integer part is 1. This is the second binary digit.
The new fractional part is 0.00.
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Since the fractional part is now 0, the conversion process is complete.
Final Binary Result
Reading the integer parts obtained in order (from top to bottom), we get 11.
Therefore, the decimal fraction 0.75 is equivalent to the binary fraction 0.11.
The conversion can be written as:
$(0.75)_{10} = (0.11)_2$
Important Questions from Miscellaneous
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