The binary number system contains two numbers 0 and 1. It is also called base two number system. Digital electronics, computers, etc. are based on the binary number system. In computer language binary also called as bit. A binary number can be converted into decimal, hexadecimal and so on.

General binary to decimal chart is given below,

 Binary 0 1 10 11 100 101 110 111 1000 1001 Decimal 0 1 2 3 4 5 6 7 8 9

0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 0 [carry out 1]
1 + 1 + 1 = 11 [carry out 1]

Subtraction rules of binary,

0 - 0 = 0
0 - 1 = 1[borrow carry 1 from left]
1 - 0 = 1
1 - 1 = 0

## Binary Formula Examples

Some solved examples of binary formula are given below:

Question 1: Add given binary numbers $(1001100)_{2}$ and $(1000000)_{2}$ .
Solution:
Given numbers $(1001100)_{2}$ and $(1000000)_{2}$

carry 1
1001100
+  1000000
--------------
10001100

Result of $(1001100)_{2} + (1000000)_{2} = (10001100)_{2}$

Question 2: Subtract given binary numbers $(1001110)_{2}$ and $(1000000)_{2}$ .
Solution:
Given numbers $(1001110)_{2}$ and $(1000000)_{2}$

Borrow
1001110
-   1000000
--------------
0001110

Result of $(1001110)_{2} + (1000000)_{2} = (0001110)_{2}$