Question

Represent the following decimal numbers in binary using 8-bit signed magnitude, one's complement, and two's complement:

a) 77
b) -42
c) 119
d) -107

Answer 1

To represent decimal numbers in binary, 8-bit signed magnitude requires the first bit for the sign and the next seven for the value, while one's and two's complement involve bit inversion and addition for negative numbers.

Step-by-step explanation:

The question asks to represent the decimal numbers 77, -42, 119, and -107 in binary using three different methods: 8-bit signed magnitude, one's complement, and two's complement. Here's how to convert each number:

8-bit Signed Magnitude

In signed magnitude, the first bit represents the sign (0 for positive, 1 for negative) and the remaining bits represent the magnitude.

• 77: 01001101
• -42: 10101010
• 119: 01110111
• -107: 11010101

One's Complement

In one's complement, negative numbers are formed by inverting all bits of their positive counterparts.

• 77: 01001101
• -42: 11010101
• 119: 01110111
• -107: 10101010

Two's Complement

In two's complement, negative numbers are formed by inverting all bits of their positive counterparts and adding one to the result.

• 77: 01001101
• -42: 11010110
• 119: 01110111
• -107: 10101011