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  10  11  100  101  110  111 1000  1001 
Decimal

Addition rules of binary,

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

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