GATE CS 2000 Q1.6 — Number Representations (Fixed and Floating Point)

To represent the decimal number $+43$ in $8$-bit $2$'s complement representation:

1. Identify the sign: The number $+43$ is positive. In $2$'s complement representation, positive numbers are represented in the same way as their standard unsigned binary representation, with the most significant bit (MSB) set to $0$.
2. Convert to binary: $$43 = 32 + 8 + 2 + 1 = 2^5 + 2^3 + 2^1 + 2^0$$ In binary, this is $101011_2$.
3. Pad to 8 bits: Extending $101011_2$ to an $8$-bit format by adding leading zeros gives: $$00101011_2$$

Thus, the $2$'s complement representation of $43$ is $00101011$.

Note: Option B ($11010101$) represents $-43$ in $2$'s complement form.