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Bitwise Operators - Programming

Q1:

Assuming a integer 2-bytes, What will be the output of the program? 
#include<stdio.h>

int main()
{
    printf('%x\n', -1<<3);
    return 0;
}

A ffff

B fff8

C 0

D -1

ANS:A - ffff

The system will treat negative numbers in 2's complement method.

Example:

Assume the size of int is 2-bytes(16 bits). The integer value 1 is represented as given below:

Binary of 1: 00000000 00000001 (this is for positive value of 1)

1's complement of binary 1: 11111111 11111110
2's complement of binary 1: 11111111 11111111

Thy system will store '11111111 11111111' in memory to represent '-1'.

If we do left shift (3 bits) on 11111111 11111111 it will become as given below:

11111111 11111111 ---(left shift 3 times)---> 11111111 11111000.

So, 11111111 11111000 ---(binary to hex)---> FF F8. (Required Answer)

Note:

How is the negative number obtained from 2's complement value?

As stated above, -1 is represented as '11111111 11111111' in memory.

So, the system will take 2's complement of '11111111 11111111' to the get the original negative value back.

Example:

Bit Representation of -1: 11111111 11111111

Since the left most bit is 1, it is a negative number. Then the value is

1's complement: 00000000 00000000
2's complement: 00000000 00000001 (Add 1 to the above result)

Therefore, '00000000 00000001' = 1 and the sign is negative.

Hence the value is -1.