UGC NET CSE | June 2012 | Part 2 | Question: 35

Question

If an integer needs two bytes of storage, then the maximum value of signed integer is

• A. $2^{16}-1$
• B. $2^{15}-1$
• C. $2^{16}$
• D. $2^{15}$

Answer 1

In case of signed Magnitude Representation the range is from  $-(2^{n-1}-1)$ to $2^{n-1}-1$

Min number that can be represented in this system is $-(2^{n-1}-1)$

The max number that can be represented in this system is  $2^{n-1}-1$

In the case of 2's complement no system, the range is from $-(2^{n-1})$ to $2^{n-1}-1$

Min no that can be represented in this system is $-(2^{n-1})$

Max no that can be represented in this system is $2^{n-1}-1$

As they said 2 Bytes = 16 bits

we can use max no that can be represented here  which is $2^{n-1}-1\implies 2^{16-1}-1=2^{15}-1$

Answer 2

Option(B)2¹⁵-1