Question

Find the two's complement binary number representation of -42 (decimal) using 8-bit numbers.

Answer 1

The two's complement binary representation of -42 is 11010110 when using an 8-bit number format. This is obtained by converting 42 to binary, inverting the digits, and then adding 1 to the result.

Step-by-step explanation:

To find the two's complement binary number representation of -42 using 8-bit numbers, follow these steps:

1. Convert the absolute value of the number to binary - 42 in decimal is 00101010 in binary.
2. Invert the digits (0s become 1s and vice versa) to get the complement - the inverted number of 00101010 is 11010101.
3. Add 1 to the inverted number to obtain the two's complement - adding 1 to 11010101 results in 11010110.

Therefore, the two's complement binary representation of -42 as an 8-bit number is 11010110.