Question

Conversion of decimal number 100 to Octal and Hexadecimal is ______ and ______

• A. \( 123_{(8)}, AB_{(16)} \)
• B. \( 64_{(8)}, 144_{(16)} \)
• C. \( 144_{(8)}, 64_{(16)} \)
• D. \( 74_{(8)}, A1_{(16)} \)

Hint:

To convert a decimal number to another base, repeatedly divide the number by the new base and record the remainders. The digits in the new base are the remainders in reverse order of their calculation. Remember to use hexadecimal digits A-F for remainders 10-15.

Answer 1

The Correct Option is C

Conversion of Decimal Number 100 to Octal and Hexadecimal

Conversion to Octal (Base-8)

We perform successive divisions by 8 and record the remainders:

• 100 ÷ 8 = 12, remainder = 4
• 12 ÷ 8 = 1, remainder = 4
• 1 ÷ 8 = 0, remainder = 1

Reading the remainders from bottom to top, the octal representation of 100 is 144₈.

Conversion to Hexadecimal (Base-16)

We perform successive divisions by 16 and record the remainders. For remainders 10–15, we use hexadecimal digits A–F:

• 100 ÷ 16 = 6, remainder = 4
• 6 ÷ 16 = 0, remainder = 6

Reading the remainders from bottom to top, the hexadecimal representation of 100 is 64₁₆.

Final Answer

Therefore, the decimal number 100 is represented as:

• 144 in Octal (Base-8)
• 64 in Hexadecimal (Base-16)

This corresponds to option (3).