GATE Bits 01 02 Number System || Lesson 26.1 || Digital Electronics || Learning Monkey ||

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Electronics

We will understand GATE Bits 01 02 Number System

01. Consider n-bit (including the sign bit) 2’s complement representation of integer numbers. The range of integer values, N, that can be represented is _____ ≤N≤_____.

[ GATE 94 ]

ANS: -2n-1 less= N less= 2n-1 -1

Explanation:

let we have 3-bit binary number (unsigned )

000 (0) to 111(7) total of 8 (23) no.

but when we have one signed bit then we have half of negative -4 to -1 and 0 and 1 to 3.

02. The number of 1’s in the binary representation of (3∗4096+15∗256+5∗16+3)

are: [ GATE 95 ]

a. 8 b. 9 c. 10 d. 12

ANS: C

Explanation:

The given number is a hexadecimal number ( 3E53 ) 16.

Hexa to binary is ( 0011111101010011 )2.

The number of 1’s is 10.

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