What is the 2’s complement of (−28)₁₀ in 16-bit representation?

To find the 16-bit 2’s complement representation of $(-28)_{10}$, we follow a standard three-step process:

1. Convert the absolute value to binary

First, find the binary representation of 28.

28 = 16 + 8 + 4

In binary: 11100

For a 16-bit representation, pad with leading zeros:

0000 0000 0001 1100

2. Find the 1's complement

Invert all the bits (change 0s to 1s and 1s to 0s):

1111 1111 1110 0011

3. Find the 2's complement

Add 1 to the 1's complement result:

1111 1111 1110 0011 + 1 = 1111 1111 1110 0100.

The 16-bit 2’s complement of (−28)₁₀ is 1111 1111 1110 0100.