Final answer:
The 2's complement representation of -122 in 32 bits is created by converting 122 to a binary number, standardizing it to 32 bits, inverting the bits, and then adding one, resulting in the final binary number 11111111111111111111111110000110.
Step-by-step explanation:
The 2's complement representation of -122 in 32 bits involves first finding the binary equivalent of the positive number, then inverting the bits and adding one to the result.
To represent -122 using 2's complement in 32 bits:
- Convert 122 to binary, which is 01111010.
- Standardize it to 32 bits: 00000000000000000000000001111010.
- Invert the bits (0s to 1s and 1s to 0s): 11111111111111111111111110000101.
- Add one to the inverted binary number: 11111111111111111111111110000110. This is the 32-bit 2's complement representation of -122.
The 2's complement representation of -122 in 32 bits is obtained by representing the positive value of 122 in binary and then taking the complement of it. To represent 122 in binary, we divide it successively by 2 and note the remainders. This gives us 1111010 in binary.
To obtain the 2's complement, we take the complement of each bit (0 becomes 1, and 1 becomes 0) and then add 1 to the least significant bit. Thus, the 2's complement of 1111010 is 0000101.
Therefore, the 2's complement representation of -122 in 32 bits is: 11111111111111111111111110000101.