Question

The binary representation of the decimal number 125 is

• A. 1110001
• B. 1010101
• C. 1111101
• D. 1111001

Hint:

When converting from decimal to binary, repeatedly divide by 2 and use the remainders to form the binary number.

Answer 1

The Correct Option is B

Step 1: Conversion from decimal to binary.
To convert 125 to binary, we divide the number by 2 and record the remainders: \[ 125 \div 2 = 62 \quad \text{remainder} \, 1 \] \[ 62 \div 2 = 31 \quad \text{remainder} \, 0 \] \[ 31 \div 2 = 15 \quad \text{remainder} \, 1 \] \[ 15 \div 2 = 7 \quad \text{remainder} \, 1 \] \[ 7 \div 2 = 3 \quad \text{remainder} \, 1 \] \[ 3 \div 2 = 1 \quad \text{remainder} \, 1 \] \[ 1 \div 2 = 0 \quad \text{remainder} \, 1 \] Reading the remainders from bottom to top, we get \( 1111101_2 \).
Step 2: Conclusion.
Therefore, the binary representation of 125 is 1111101.