Question

What is the 2's complement of the binary number 1011001?

• A. 0100110
• B. 0100111
• C. 0101001
• D. 1011010

Hint:

Shortcut for 2's complement: Scan the binary number from right to left. Keep all bits the same up to and including the first '1', then invert all the remaining bits to the left.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
We must determine the 2's complement representation of the binary sequence 1011001.
Step 2: Key Formula or Approach:
The standard method to find the 2's complement involves two steps:
1. Compute the 1's complement by toggling every bit (0 becomes 1, and 1 becomes 0).
2. Add 1 to the least significant bit (LSB) of the resulting 1's complement.
Step 3: Detailed Explanation:
The initial binary value is \(1011001\).
Step 1: Invert all bits to get the 1's complement:
Original: \(1 \quad 0 \quad 1 \quad 1 \quad 0 \quad 0 \quad 1\)
1's comp: \(0 \quad 1 \quad 0 \quad 0 \quad 1 \quad 1 \quad 0\)
Step 2: Add 1 to this 1's complement value:
\[ 0100110 + 1 = 0100111 \] The final 2's complement is \(0100111\).
Step 4: Final Answer:
The correct choice is (B).