GATE Papers >> CSE >> 2016 >> Question No 119

Question No. 119 CSE | GATE 2016

Let X be the number of distinct 16-bit integers in 2's complement representation. Let Y be the number of distinct 16-bit integers in sign magnitude representation. Then X-Y is ________.


Answer : 1.0 : 1.0


Solution of Question No 119 of GATE 2016 CSE Paper

Number of bits n = 16

In sign 2's complement  representation the range is 

               = -215 to + (215 - 1)

               = -32768 to + 32767

$\therefore$         X = 65536

In sign magnitude represntation the range is

               = (215 - 1) to + (215 - 1)

               = -32767 to + 32767

$\therefore$         Y = 65536 

Hence

X - Y = 1

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