# Binary Subtraction

Binary subtraction is another basic binary operation. The basic operations in mathematics are addition, subtraction, multiplication, and division. To recall, binary operation represents the operations of mathematics that are performed on two operands and the result is obtained.

## 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

## How to Subtract Binary Numbers?

Learn how to do binary subtraction using the example: 1010 – 101

### Procedure to do Binary Subtraction:

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.

### Examples on Binary Subtraction

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 = 34_{10}

(-) 0 0 0 1 0 1 0 = 10_{10}

——————

0 0 1 1 0 0 0 = 24_{10}

## 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.

### Binary Subtraction Questions Using 1’s Compement

**Question 1:**

(110101)_{2} – (100101)_{2}

**Solution:**

(1 1 0 1 0 1)_{2 }= 53_{10}

(1 0 0 1 0 1)_{2 }= 37_{10} – 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 } = 16_{10}

**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}.

## Frequently Asked Questions

### What is Binary Subtraction?

Binary subtraction, unlike decimal subtraction involves only two digits i.e. 0 and 1.

### What are the Rules of Binary Subtraction?

There are four rules of binary subtraction which are:

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