Binary Subtraction Definition, Table, Rules, Examples | How to Subtract Binary Numbers?

Binary Subtraction is one among the four binary operations in which we perform subtraction of binary numbers i.e. 0 or 1. It is similar to the Basic Arithmetic Operation of Decimals. When we subtract 1 from 0 we need to borrow 1 from the next digit to reduce the digit by 1 and the remainder left here is 1. Go through the entire article to know about Binary Subtraction Rules, Subtraction Table, Tricks and Procedure on How to Subtract Binary Numbers, etc.

What is meant by Binary Subtraction?

Binary Numbers Subtraction is similar to Subtraction of Decimals or Base 10 Numbers. For instance, 1+1+1 is 3 in base 10 whereas in a binary number system 1+1+1 is 11. While Performing Addition and Subtraction in Binary Numbers be careful with borrowing as you might need to do them quite often.

While performing subtraction of several columns of binary digits you need to consider the borrowing. If you subtract 1 from 0 the result will be 1 where 1 is borrowed from the next highest order digit.

Binary Subtraction Table

Binary Number Subtraction Value
0 – 0 0
1 – 0 1
0 – 1 1 (Borrow 1 from next high order digit)
1 – 1 0

On Adding Two Binary Numbers 1 and 1 we get the result 10 in which we consider 0 and carry forward 1 to the next higher-order bit. On Subtracting 1 from 1, the result is 0 and nothing will be carry forwarded.

While subtracting 1 from 0 in the case of decimal numbers we borrow 1 from the preceding higher-order number and make it 10 and after subtracting result becomes 9. However, in the case of Binary Subtraction, the result is 0.

Rules for Binary Subtraction

Binary Subtraction is quite simple compared to Decimal Subtraction if you remember the following tips and tricks.

0 – 0 = 0
0 – 1 = 1 ( with a borrow of 1)
1 – 0 = 1
1 – 1 = 0

You can look at the binary subtraction examples provided below for better understanding.

How to Subtract Binary Numbers?

Follow the below-listed steps to perform Binary Subtraction. You will find the Subtraction of Binary Numbers much easier after going through the below steps. They are as follows

  • Align the numbers similar to an ordinary subtraction problem. Write the larger number up and the smaller number below it. If the Smaller Digit has few digits align them towards the right same as in decimal subtraction.
  • Begin from the right column and perform the subtraction operation of binary numbers. While doing so keep the binary subtraction rules in mind and do accordingly.
  • Solve column by column moving from right to left.

Binary Subtraction Examples

1. Find the Value of 1010011 – 001110?

Solution:

Write the given numbers as if you subtracting decimal numbers. Align them to the right and fill them with leading zeros so that both the numbers have the same digits.

1011011

(-)0001010

——————

1010001

Binary Notation

Decimal Notation

The decimal Equivalent of given numbers is

1011011 = 91

001010 = 10

91-10 = 81

2. Find the value of 1100010 – 001000?

Solution:

Write the given numbers as if you subtracting decimal numbers. Align them to the right and fill them with leading zeros so that both the numbers have the same digits.

1100010

(-)0001000

——————

1,011,010

Decimal Notation

The decimal Equivalent of given numbers is

1100010 = 98

1000 = 8

98-8 = 90

Binary Subtraction using 1’s Complement

Go through the below procedure and perform the Binary Subtraction easily. They are as follows

  • Firstly, write the 1’s complement of the subtrahend.
  • And then add the 1’s complement subtrahend with the minuend.
  • If the result has a carryover add the carryover in the least significant bit.
  • If it has no carryover take the 1’s complement of resultant and it is negative.

Questions on Binary Subtraction using 1’s Complement

1. (11001)2  – (1010)2

Solution:

(11001) = 25

(1010) = 10 – subtrahend

Fill with leading zeros till you have the same number of digits in both the numbers. Firstly, take the 1’s complement of subtrahend i.e. (01010)2.

1’s complement of the subtrahend is 10101. Add 1 to the 1’s complement of the second number

10101
+   1

10110

Now instead of subtracting add the 1’s complement of the second number to the first one

11001
+ 10110

——————
101111

Remove the leading 1 to obtain the result.

Then, remove the leading zeros as it will not alter the result and you can write the final result of subtraction as such

11001
– 1010

——————

1111

FAQs on Binary Subtraction

1. What are the Rules of Binary Subtraction?

Rules of Binary Subtraction are as follows

0 – 0 = 0
0 – 1 = 1 ( with a borrow of 1)
1 – 0 = 1
1 – 1 = 0

2. How many basic binary subtraction combinations are possible?

There are four possible binary subtraction combinations when subtracting binary digits.

3. What signs does the binary digit 0 and 1 represent?

0 represents the positive sign and 1 represents the negative sign.

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