Project ForgeComputer Organization & Architecture
Memory Hierarchy & Floating Point
GATE 2014
Hard
The base (or radix) of the number system such that the following equation holds is: 312/20 = 13.1
5
Explanation
In base b: 312_b = 3b²+b+2, 20_b = 2b, 13.1_b = b+3+1/b = (b²+3b+1)/b. Setting (3b²+b+2)/(2b) = (b²+3b+1)/b and cross-multiplying: (3b²+b+2)b = 2b(b²+3b+1), i.e. 3b²+b+2 = 2b²+6b+2 (dividing by b), giving b²−5b=0, so b=5 (rejecting b=0). All digits used (max digit 3) are valid for base 5.
Source: GATE CS 2014 (Session 1) (2014)
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