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:
The question requires us to find the 2's complement of a given binary number (1011001).


Step 2: Key Formula or Approach:
To find the 2's complement of a binary number, follow these two steps:
1. Find the 1's complement by inverting all the bits (change 0 to 1 and 1 to 0).
2. Add 1 to the least significant bit (LSB) of the 1's complement.


Step 3: Detailed Explanation:
The given binary number is \(1011001\).
First, find the 1's complement by flipping all the bits:
Original: \(1 \quad 0 \quad 1 \quad 1 \quad 0 \quad 0 \quad 1\)
1's comp: \(0 \quad 1 \quad 0 \quad 0 \quad 1 \quad 1 \quad 0\)
Next, add binary \(1\) to the 1's complement:
\[ 0100110 + 1 = 0100111 \] The resulting binary number is \(0100111\).


Step 4: Final Answer:
The correct choice is (B).