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GATE 2014 CS (CS1) – Question 18

Digital Logic · Number Representation and Arithmetic · 1 mark · Numerical answer

Find the base (radix) in which 312/20 = 13.1.

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Correct answer: 5 to 5

Explanation

For radix b,312 represents3b²+b+2,20 represents2b and13.1 represents b+3+1/b. The equation gives3b²+b+2=2b²+6b+2, or b(b−5)=0. A valid radix exceeds the largest digit3, so **b=5**.