Two's complement is used to represent negative numbers in binary. Denary 8-bit two's complement binary 45 -45 -100 (a) Complete the table by converting each...
Question 1 Report
Two's complement is used to represent negative numbers in binary.
| Denary | 8-bit two's complement binary |
|---|---|
| 45 | |
| -45 | |
| -100 |
(a) Complete the table by converting each denary number to 8-bit two's complement binary. Show your working. [6]
Answer Details
(a) Converting each denary number to 8-bit two's complement binary:
45:
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
| 0 | 0 | 1 | 0 | 1 | 1 | 0 | 1 |
45 = 32 + 8 + 4 + 1 = 00101101. [2]
-45:
- Start with the positive representation: 00101101
- Flip all bits (one's complement): 11010010
- Add 1: 11010010 + 1 = 11010011
The result is 11010011. [2] This "flip and add 1" method is the standard algorithm for finding the two's complement (negative) of a binary number.
-100:
- First convert 100 to binary: 100 = 64 + 32 + 4 = 01100100
- Flip all bits: 10011011
- Add 1: 10011011 + 1 = 10011100
The result is 10011100. [2]
In two's complement, the most significant bit (MSB) indicates the sign: 0 for positive, 1 for negative. The range of an 8-bit two's complement number is -128 to +127.
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