Complement
From Compsci1
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We use complement to help store negative numbers in the computer. We use + and – to mark positive and negative numbers. However, computers can only read information in bits, 0s or 1s, so we use a new method to store negative numbers. | We use complement to help store negative numbers in the computer. We use + and – to mark positive and negative numbers. However, computers can only read information in bits, 0s or 1s, so we use a new method to store negative numbers. | ||
| - | + | <pre> | |
| - | The 1’s complement (ones complement) of a binary numbers is found by changing all the 1s to 0s and all the 0s to 1s. | + | The 1’s complement (ones complement) of a binary numbers is found |
| + | by changing all the 1s to 0s and all the 0s to 1s. | ||
1001 0011 | 1001 0011 | ||
1s complement 0110 1100 | 1s complement 0110 1100 | ||
| - | The 2’s complement (twos complement) of a binary number is found by getting the ones complement first and then adding 1. | + | The 2’s complement (twos complement) of a binary number is found |
| + | by getting the ones complement first and then adding 1. | ||
EG: | EG: | ||
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2’s complement 0011 1011 | 2’s complement 0011 1011 | ||
| - | Negative numbers are the 2’s complement of the corresponding positive number. To subtract a number, find the 2’s complement and add it. | + | Negative numbers are the 2’s complement of the corresponding positive number. |
| + | To subtract a number, find the 2’s complement and add it. | ||
Sign bit: | Sign bit: | ||
The left most bit of a binary number is the sign bit: | The left most bit of a binary number is the sign bit: | ||
0 means the number is positive | 0 means the number is positive | ||
| - | 1 means the number is negative. | + | 1 means the number is negative.</pre> |
Twos complement overflow flag: | Twos complement overflow flag: | ||
If we add or subtract numbers and part of the answer overflows the available capacity of the storage space this can cause a problem. If we add 2 negative numbers in twos complement the answer can overflow beyond the capacity and give the impression of a positive number. To catch this problem the computer has the TWOS COMPLEMENT OVERFLOW FLAG which can be written into a program and checked after an operation to see if this has happened. | If we add or subtract numbers and part of the answer overflows the available capacity of the storage space this can cause a problem. If we add 2 negative numbers in twos complement the answer can overflow beyond the capacity and give the impression of a positive number. To catch this problem the computer has the TWOS COMPLEMENT OVERFLOW FLAG which can be written into a program and checked after an operation to see if this has happened. | ||
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Current revision as of 20:08, 11 October 2006
COMPLEMENT
We use complement to help store negative numbers in the computer. We use + and – to mark positive and negative numbers. However, computers can only read information in bits, 0s or 1s, so we use a new method to store negative numbers.
The 1’s complement (ones complement) of a binary numbers is found by changing all the 1s to 0s and all the 0s to 1s. 1001 0011 1s complement 0110 1100 The 2’s complement (twos complement) of a binary number is found by getting the ones complement first and then adding 1. EG: Binary number 1100 0101 1’s complement 0011 1010 + 1 _______ 2’s complement 0011 1011 Negative numbers are the 2’s complement of the corresponding positive number. To subtract a number, find the 2’s complement and add it. Sign bit: The left most bit of a binary number is the sign bit: 0 means the number is positive 1 means the number is negative.
Twos complement overflow flag: If we add or subtract numbers and part of the answer overflows the available capacity of the storage space this can cause a problem. If we add 2 negative numbers in twos complement the answer can overflow beyond the capacity and give the impression of a positive number. To catch this problem the computer has the TWOS COMPLEMENT OVERFLOW FLAG which can be written into a program and checked after an operation to see if this has happened.
