Question

Convert the following decimal numbers into 8-bit signed binary numbers:

(a) +32
(b)-12
(c) +100
(d) -92

Answer 1

To convert decimal numbers to 8-bit signed binary, convert the absolute value to binary, add a leading sign bit (0 for positive, 1 for negative), and for negative numbers, take the two's complement.

Step-by-step explanation:

The question asks to convert decimal numbers into 8-bit signed binary numbers. Here's how you convert them:

(a) +32: First, find the binary equivalent of the positive decimal number 32, which is 100000 in binary. Since it is an 8-bit signed binary number and it is positive, the first bit is 0, giving us 00100000.

(b) -12: For negative numbers, first find the binary equivalent of the positive version, which for 12 is 1100. Next, find the two's complement by inverting the digits and adding one to get the negative representation. This gives us 11110100.

(c) +100: The positive decimal 100 is 1100100 in binary. Adding the leading zero for the sign bit, we get 01100100.

(d) -92: The positive binary equivalent of 92 is 1011100. After inverting the digits and adding one for the two's complement, we get 10110100.