Binary Subtraction

The basic operations in mathematics are addition, subtraction, multiplication, and division. The term “Binary operation” represents the operations of mathematics that are performed on two operands and the result is obtained. In this section, we will discuss a binary subtraction operation in detail, including:

  • What is Binary Subtraction? Procedure to subtract two binary numbers.
  • Examples on Subtracting two Binary Numbers

What is Binary Subtraction?

Can you subtract binary numbers? The answer is yes. Subtraction of binary numbers is an arithmetic operation similar to the subtraction of base 10 numbers. For example, 1 + 1 + 1 = 3 in base 10  and 1 + 1 + 1 = 11 in binary number system. When you add and subtract binary numbers you will need to be careful when  borrowing as these will take place more often. 

When you subtract several columns of binary digits, you must take into account the borrowing. when 1 is to be subtracted from 0, the result is 1 with borrowed from the previous position.

Binary Subtraction Rule Chart

Rules and tricks: Binary subtraction is much easier than the decimal subtraction when you remember the following rules:

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

Now, look at the example of the binary subtraction: 101 from 1010

Procedure:

1010

(-) 101

Step 1: First consider the 1’s column, and subtract the one’s column,( 0 – 1 ) and it gives the result 1 as per the condition of binary subtraction with a borrow of 1 from the 10’s place.

Step 2: After borrowed 1 from the 10’s column, the value 1 in the 10’s column is changed into the value 0

1 Borrow

1 0 1 0

(-) 1 0 1

——————

1

Step 3: So, subtract the value in the 10’s place, ( 0 – 0 ) = 0.

1 Borrow

1 0 1 0

(-) 1 0 1

——————

0 1

Step 4: Now subtract the values in 100’s place. Borrow 1 from the 1000’s place ( 0 – 1 ) = 1.

1 1 Borrow

1 0 1 0

(-) 1 0 1

——————

0 1 0 1

So, the resultant of the subtraction operation is 0101.

When you cross-check the binary subtraction resultant value with the decimal value, the resultant value should be the same.

The binary value 1010 is equal to the decimal value 10 and 101 is equivalent to 5

So, 10 – 5 = 5

Therefore, the decimal number 5 is equal to the binary number 0101.

Consider other examples of binary subtractions are as follows:

Example 1: 0011010 – 001100

Solution:

1 1 Borrow

0 0 1 1 0 1 0

(-) 0 0 1 1 0 0

——————

0 0 0 1 1 1 0

Decimal Equivalent :

0 0 1 1 0 1 0 = 26

0 0 1 1 0 0 = 12

Therefore 26 – 12 = 14

The binary resultant 0 0 0 1 1 1 0 is equivalent to the 14

Example 2: 0100010 – 0001010

Solution:

1 1 Borrow

0 1 0 0 0 1 0 = 3410

(-) 0 0 0 1 0 1 0 = 1010

——————

0 0 1 1 0 0 0 = 2410

Binary Subtraction Using 1’s Complement

The number “ 0 “ represents the positive sign

The number “ 1 “ represents the negative sign

Procedures for Binary Subtraction by 1’s Complement

  • Write the 1’s complement of the subtrahend
  • Then add the 1’s complement subtrahend with the minuend
  • If the result has a carryover, then add that carry over in the least significant bit
  • If there is no carryover, then take the 1’s complement of the resultant and it is negative.

Sample Examples

Question 1:

(110101)2 – (100101)2

Solution:

(1 1 0 1 0 1)2 = 5310

(1 0 0 1 0 1)2 = 3710 – subtrahend

Now take the 1’s complement of the subtrahend and add with minuend.

1 carry

1 1 0 1 0 1

(+) 0 1 1 0 1 0

——————

0 0 1 1 1 1

1 carry

——————

0 1 0 0 0 0

Therefore, the solution is 010000

(010000)2 = 1610

Question 2:

(101011)2 – (111001)2

Solution

Take 1’s complement of the subtrahend

1 1 1

1 0 1 0 1 1

(+) 0 0 0 1 1 0 (1’s complement)

——————

1 1 0 0 0 1

Now take the 1’s complement of the resultant since it does not carry 1

The resultant becomes 0 0 1 1 1 0

Now, add the negative sign to the resultant value

Therefore the solution is – (001110)2.

For more information on binary operations like addition, multiplication, and division operations register with BYJU’S – The Learning App and also watch interesting videos to learn with ease.

 

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