Convert -52 (base 10) to binary 8-bit one’s complement. explain
The correct answer and explanation is :
To convert -52 (base 10) to an 8-bit one’s complement binary representation, let’s break down the steps carefully:
Step 1: Convert the positive integer (52) to binary.
First, we convert 52 into its binary form. In base 10, 52 can be broken down into powers of 2:
- 52 ÷ 2 = 26, remainder 0
- 26 ÷ 2 = 13, remainder 0
- 13 ÷ 2 = 6, remainder 1
- 6 ÷ 2 = 3, remainder 0
- 3 ÷ 2 = 1, remainder 1
- 1 ÷ 2 = 0, remainder 1
So, 52 in binary is 110100.
Since we need an 8-bit representation, we add two leading zeros to make it an 8-bit binary number. This gives us:
00110100
Step 2: Apply one’s complement to the binary number for negative value.
One’s complement is a way to represent negative numbers in binary. To find the one’s complement of a number, we invert all the bits (i.e., change 0 to 1 and 1 to 0).
For the positive binary number 00110100, we invert each bit:
- 0 becomes 1
- 0 becomes 1
- 1 becomes 0
- 1 becomes 0
- 0 becomes 1
- 1 becomes 0
- 0 becomes 1
- 0 becomes 1
This gives us the binary one’s complement representation of -52:
11001011
Explanation of one’s complement:
The one’s complement is used to represent negative numbers in binary. It works by inverting all the bits of the positive number. However, one’s complement has an issue: it has two representations for zero (positive zero and negative zero), which can lead to complications in certain arithmetic operations. In one’s complement, to represent -52, we start with the binary representation of +52 and invert the bits to get 11001011. This is how negative numbers are stored using one’s complement in an 8-bit system.
Thus, the 8-bit one’s complement representation of -52 is 11001011.