NIMCET 2007 — Computer PYQ

In modern digital computer systems, negative integers are typically stored and manipulated using the 2's complement representation within a fixed-size register (most commonly an $8$-bit format for standard textbook problems). Let's determine how $(-1{)}_{10}$ is encoded.

Step 1: Write the Binary representation of the Positive Magnitude

First, write out the value of the positive number $+1$ in an $8$-bit binary format:

$$(+1{)}_{10}=(00000001{)}_2$$

Step 2: Find the 1's Complement

To find the 1's complement, invert all the bits (change every $0$ to $1$ and every $1$ to $0$):

$$\text{1’s complement of }00000001_2=11111110_2$$

Step 3: Find the 2's Complement

To arrive at the 2's complement representation, add $1$ to the 1's complement value:

$$11111110_2+1_2=11111111_2$$

Thus, the standard 2's complement notation for $(-1{)}_{10}$ is $(11111111{)}_2$.