Question

Convert the binary number \(1101101\) to hexadecimal. Which of the following options is correct ?

• A. \(3A\)
• B. \(155\)
• C. \(6D\)
• D. \(5C\)

Hint:

Binary to hexadecimal conversion: \[ 1\ \text{hex digit} = 4\ \text{binary bits} \] Always group bits from right to left.

Answer 1

The Correct Option is C

Concept: Hexadecimal number system uses base: \[ 16 \] Each hexadecimal digit corresponds to: \[ 4\ \text{binary bits} \] Therefore binary-to-hex conversion is done by grouping bits into sets of four.

Step 1: Write the binary number. Given binary number: \[ 1101101 \]

Step 2: Group bits into 4-bit groups from right side. Add leading zero if necessary: \[ 0110\ 1101 \] Now there are two groups: \[ 0110 \quad \text{and} \quad 1101 \]

Step 3: Convert each group to hexadecimal. For: \[ 0110 \] binary equivalent is: \[ 6 \] For: \[ 1101 \] binary equivalent is: \[ 13 \] Hexadecimal representation of 13 is: \[ D \] Therefore: \[ 1101101_2 = 6D_{16} \]

Step 4: Write final answer. Hence the hexadecimal equivalent is: \[ \boxed{6D} \] Therefore the correct option is: \[ \boxed{(C)} \]