**Binary subtraction** is one of the four binary functions, in which we perform a two-digit **binary subtraction** (which includes only two digits, 0 and 1). This function is similar to the arithmetic subtraction performed on decimal numbers in Mathematics. When we subtract “1” from “0”, we need a borrow “1” from the next higher order. in order to reduce the digit by 1 and the remainder left here is also 1.

**Example of binary subtraction**:

- 0 – 0 = 0
- 1 – 0 = 1
- 1 – 1 = 0
- 0 – 1 = 1 (Borrow 1)

Binary subtraction is the process of extracting binary numbers. Binary numbers has two bits and that bit are “0” and “1”. The binary subtraction process is similar to the arithmetic of arithmetic operations we do with numbers. Since only two binary bit that are “0” and “1” involved here. So, we need to subtract 0 from 1. In such cases, we use the concept of borrowing as we do in arithmetic removal. The binary number is defined by base 2. Let us see some example, a binary number is written as (101)_{ 2 .}

**Binary Subtraction Rules**

There are some rules of binary subtraction which are given below:

- 0 – 0 = 0
- 1 – 0 = 1
- 1 – 1 = 0
- 0 – 1 = 1 (Borrow 1 from next binary bit)

**How To Do Binary Subtraction?**

Decimal or base 10 numbers can be denoted in binary numbers with only two number and that are “0” and “1”. Binary bit only use in digital computer or digital communication because they only understand binary digits, 0 and 1. Let’s see the some example of binary subtraction or how to subtract binary numbers from shown below.

**Binary withdrawals without borrowing**

Subtract (1 0 0)_{2 }from (1 1 1 1)_{2 }

Arrange the numbers and follow the rules of binary subtraction to extract the result. In this minus, we do not associate the minus 1 to 0. So, the difference is (1 0 1 1)_{2 }

(1 1 1 1)_{2 } – (1 0 0)_{2 } = (1 0 1 1)_{2 }

**Binary subtraction with borrowing**

Subtract (1 0 1)_{2 }– (1 0 0 1)_{2 }

Arrange the numbers and follow the rules of binary subtraction to extract the result. In this minus, we do not associate the minus 1 to 0. So, the difference is (1 0 1 1)_{2 }

(1 0 0 1)_{2 } – (1 0 1)_{2 } = (1 0 0)_{2 }

Follow the rules of subtraction to extract result. In this subtraction operation, firstly move the numbers from the right to the next higher order digit. The first step is to extract (1-1). This is equal to 0. Similarly, we move on to the next top order digit and subtract (0 – 0), which is 0. In the next step, we have to subtract (0 – 1), so we borrow 1 digit for the next order. Therefore, the output value (0 – 1) is 1.

**Binary ****Subtraction ****using 1’s Complement**

The 1’s complement of the number is obtained by alternating from 0 to 1 and every 1 to 0 in the binary number. For example (1 1 0)_{2 }is ( 0 0 1)_{2 }. The number **0** represents the positive sign and **1** represents the negative sign

**Procedures for Binary Subtraction by 1’s Complement**

- Convert the subtrahend in the 1’s complement number.
- After convert to 1’s complement number add the 1’s complement subtrahend with the minuend
- If the results produce carryover, then add that carry over in the least significant bit.
- If the result not produce carryover, then take the 1’s complement of the resultant, and it is negative

**Example of ****Subtraction by 1’s Complement**

**Question **

(110101)_{2} – (100101)_{2}

**Answer **

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

37_{10} = (1 0 0 1 0 1)_{2 } (it is a subtrahend)

Now take the 1’s complement of the (1 0 0 1 0 1)_{2 } and substract.

1 carry

(1 1 0 1 0 1)_{2 } (+) (0 1 1 0 1 0)_{2 }= (0 0 1 1 1 1)_{2}

“1” has carry this carry and this carry add to the result again to obtain the result

(0 0 1 1 1 1)_{2 }+ (0 0 0 0 0 1)_{2 }= (0 1 0 0 0 0)_{ 2}

Therefore, the solution is 010000

(010000)_{2 }= 16_{10}

**frequently ask question.**

**What is binary binary 101001 010110?**

Question: – the binary subtraction operation of this bits is101001-010110 → 010011 (Answers)

### Step by step the process of converting decimal to a binary system is:

- Find 2 maximum power within a given number.
- Subtract that number from the given number.
- Find the 2 main forces in the remainder found in step 2.
- Repeat until there is nothing left.

**What is binary add and subtraction?**

Addition and subtraction of data is the same as the decimal number system. But the main difference between the two is that the binary number system uses two digits as 0 & 1 while the decimal number system uses the digits from 0 to 9 and the base for this is 10.