If the 2's complement representation of a number is (011010)₂ , what is its equivalent hexadecimal representation?

Concept:

1. Signed magnitude representation uses the most significant bit (MSB) a sign bit.

• If the sign bit is ‘0’ then the number is positive.
• If the sign bit is ‘1’ then the number is negative.

The remaining bits represent the magnitude of the binary number.

2. 1’s complement representation:

It is a representation of a binary number obtained by toggling all bits in it i.e. transforming the 0 bit to 1 and the 1 bit to 0.

3. 2’s complement representation:

It is obtained by simply adding 1 to the 1’s complement of that binary number.

Note: 

To find the original binary number from the 2’s complement representation

Step 1: Subtract one (1) from 2’s complement representation.

Step 2: Toggle the resultant.

Calculation:

2's complement representation of a number = (011010)2

Subtracting 1 from number ⇒ (011010)2 - (1)2 = (011001)2

Toggle the resultant ⇒ (011001)2 → (100110)2

(0010 0110)2 = (26)₁₆

∴ The correct answer is (26)16