Question

What is the 8-bit binary (two's-complement) representation of

each of the following signed decimal integers?
a. 5
b. 42

Answer 1

To express signed decimal integers in 8-bit binary two's complement format, convert them to their binary equivalent, extend to 8 bits if necessary, and for negative numbers, invert the bits and add 1. For example, the 8-bit two's complement representations of 5 and 42 are 00000101 and 00101010, respectively.

Step-by-step explanation:

To convert signed decimal integers to their equivalent 8-bit binary (two's complement) representation, we can use the following steps:

1. Convert the absolute value of the decimal number to binary.
2. Fill additional bits to the left to make it an 8-bit number, if necessary.
3. If the number is positive, the most significant bit (MSB) is 0. If the number is negative, invert all bits and add 1 to get the two's complement.

For the signed decimal integer 5, in binary, we get 101. Filled to 8 bits, it is 00000101. Since 5 is positive, the MSB remains 0, so the 8-bit two's complement representation is 00000101.

For the signed decimal integer 42, in binary, we get 101010. Filled to 8 bits, it is 00101010. Since 42 is positive, the MSB remains 0, so the 8-bit two's complement representation is 00101010.