Table of Contents
An Introduction to Binary Subtraction
Binary subtraction is the process of subtracting two binary numbers. The two numbers are represented by two strings of 0s and 1s, with a 1 representing a number and a 0 representing a space. The number being subtracted is represented by the first string of digits and the number being subtracted from it is represented by the second string of digits.
To subtract two binary numbers, first subtract the rightmost 1s from the two numbers. If the result is 0, then the numbers are the same. If the result is a 1, then the number being subtracted from is larger. In this case, subtract the leftmost 1 from the number being subtracted from to get the final result.
For example, to subtract 101 from 111, subtract the rightmost 1s from 101 and 111. This gives a result of 0, so the numbers are the same.
What is Binary Subtraction?
Binary subtraction is the process of subtracting two binary numbers. In binary subtraction, each number is represented by a string of 0s and 1s. The first number is subtracted from the second number, and the difference is computed by finding the difference between the two binary representations.
Binary Subtraction Rules
To subtract two binary numbers, first subtract the ones column. If the number in the ones column is the same for both numbers, then subtract the tens column. If the number in the tens column is the same for both numbers, then subtract the hundreds column, and so on.
For example, to subtract 1011 from 1000, first subtract 1 from 1 in the ones column, which leaves 0. Then subtract 1 from 0 in the tens column, which leaves -1. Finally, subtract 1 from -1 in the hundreds column, which leaves 8. Therefore, the final answer is 800.
Example of Subtraction of Binary Numbers
The following is an example of subtracting binary numbers:
1010 – 1100
The answer is 1010 – 1100 = 10.
How do you Subtract Binary Numbers?
To subtract binary numbers, you convert the numbers to decimal, and then subtract the decimal values.
Binary Subtraction Example
Subtracting binary numbers is the same as subtracting regular numbers, except you have to use the binary representation of the numbers.
For example, to subtract 5 from 3, you would use the binary representation of 5 (101) and 3 (011), and the answer would be 2 (0010).
Subtraction using 1’s Complement
To subtract two numbers using 1’s complement, we take the 1’s complement of the first number, add it to the second number, and then take the 1’s complement of the result.
For example, to subtract 5 from 12, we take the 1’s complement of 5 (which is 1010), add it to 12 (which is 1100), and then take the 1’s complement of the result (which is 0101). So the final answer is 7.
5 – 12 = 7
Binary Subtraction Rules by 1’s Complement
To subtract two binary numbers using 1’s complement, follow these steps:
1. Invert the second number (flip all the bits).
2. Add the two numbers together.
3. Invert the result (flip all the bits).
For example, to subtract 1010 (decimal 10) from 1111 (decimal 15), follow these steps:
1. Invert the second number (flip all the bits): 0111
2. Add the two numbers together: 0101
3. Invert the result (flip all the bits): 1000
Binary Subtraction Examples using 1’s Complement
The following are examples of binary subtraction using 1’s complement.
1’s complement of 5 is 1010
1’s complement of 4 is 1000
1’s complement of 3 is 1101
1’s complement of 2 is 1100
1’s complement of 1 is 1011
1’s complement of 0 is 1000
