← 2024 Paper 2

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

5 marks · Section B

Number systems · Numerical Analysis · asked 7× in 13 yrs · Read the full method →

Question

Determine the decimal equivalent of $(9B2.1A)_{16}$.

Technique

Direct expansion in powers of $16$; $A=10$, $B=11$.

Solution

Term by term:

• $9\cdot 4096=36864$
• $11\cdot 256=2816$
• $2\cdot 16=32$
• $1/16=0.0625$
• $10/256=0.0390625$

Integer part: $36864+2816+32=39712$. Fractional part: $0.0625+0.0390625=0.1015625$.

Answer