NIMCET 2027 1s Complement 2s Complement Previous Year Questions (PYQs) – Page 3 of 3

In $n$-bit $2$'s complement representation, the range of signed integers is:

$-2^{n-1}$ to $2^{n-1}-1$

Here,

$n=8$

So, range is:

$-2^{7}$ to $2^{7}-1$

$=-128$ to $127$

Therefore, the minimum negative integer value is $-128$.

Given $8$-bit two's complement number is:

$11010011$

Since the leftmost bit is $1$, the number is negative.

To find its magnitude, take two's complement.

First, invert all bits:

$11010011\to 00101100$

Now add $1$:

$00101100+1=00101101$

Now convert $00101101$ to decimal:

$00101101=32+8+4+1$

$=45$

Since the original number was negative, the decimal equivalent is:

$-45$