UPSC 2024 Maths Optional Paper 2 Q5c-i — Step-by-Step Solution

5 marks · Section B

Representation of Integers, Signed Integers, and Reals (incl. Double Precision) · Numerical Analysis · Read the full method →

Question

Determine the decimal equivalent in sign-magnitude form of $(8D)_{16}$ and $(FF)_{16}$ .

Convert hex to 8-bit binary; the MSB is the sign bit; the remaining 7 bits give the magnitude.

$(8D)_{16}$ :

$8=1000_2$ , $D=1101_2$ → $(8D)_{16}=10001101_2$ .

MSB $=1$ → negative. Magnitude bits $0001101_2=8+4+1=13$ .

$(8D)_{16}\to-13$ .

$(FF)_{16}$ :

$F=1111_2$ → $(FF)_{16}=11111111_2$ .

MSB $=1$ → negative. Magnitude bits $1111111_2=127$ .

$(FF)_{16}\to-127$ .

\boxed{\;(8D)_{16}=-13,\qquad(FF)_{16}=-127\quad(\text{sign-magnitude, 8-bit}).\;}