Question

The binary representation of the decimal number 1.375 is:

• A. 1.111
• B. 1.010
• C. 1.011
• D. 1.001

Hint:

Convert fractional part: Multiply by 2, take integer part repeatedly.

Answer 1

The Correct Option is C

To convert the decimal number 1.375 into its binary representation, follow these steps:
1. Separate the integer and fractional parts of the decimal number. Here, the integer part is 1 and the fractional part is 0.375.
2. Convert the integer part (1) into binary:
    The binary representation of 1 is 1.
3. Convert the fractional part (0.375) into binary:
    a. Multiply the fractional part by 2: 0.375 × 2 = 0.75. The integer part is 0.
    b. Multiply the new fractional part by 2: 0.75 × 2 = 1.5. The integer part is 1.
    c. Multiply the new fractional part (0.5) by 2: 0.5 × 2 = 1.0. The integer part is 1.
4. Combine the results:
    The binary representation of the integer part is '1'.
    The binary sequence of fractional part from the steps above is '011'.
5. Therefore, the binary representation of 1.375 is 1.011.
The correct answer is: 1.011