Question

What is the 8-bit binary representation of the decimal number -38? (two's complement)

Answer 1

The 8-bit binary representation of the decimal number -38 in two's complement is 11011010, which is obtained by converting 38 to binary, padding to 8 bits, flipping all bits, and adding 1.

Step-by-step explanation:

To represent the decimal number -38 in 8-bit binary using two's complement, we should follow these steps:

1. Find the binary representation of the positive equivalent, which is 38. Convert 38 to binary: 38 in binary is 100110.
2. Ensure it is 8 bits by padding zeros on the left: The 8-bit binary of 38 is 00100110.
3. Flip all the bits (1 to 0 and 0 to 1, also called the one's complement): Flipping 00100110 gets us 11011001.
4. Add 1 to the result of step 3 to get the two's complement: Adding 1 to 11011001 we get 11011010, which is the 8-bit binary representation of -38.