Binary Number System

The binary number system, radix two, it uses only two characters (1, 0). For many devices such as programmable controllers and digital computers, the binary system is the most useful. It was adopted for convenience

1×8 + 1×4 + 0×2 + 1 + 1×(1/2) + 0×(1/4) + 1×(1/8)
(=13.625 in Decimal)

How to Show that a Number is Binary
The binary number follows with a little 2: 10101₂ by this way people won't think it is the decimal number "10101" (ten thousand, one hundred and one).

Conversion binary numbers into decimal
Let us take an example

Convert 1101₂   into decimal

        1*2⁰=1*1=1

+     0*2¹=0*2=0

+     1*2²=1*4=4

+    1*2³=1*8=8   ================ 13

So (1101)₂=(13)₁₀

Conversion decimal numbers into binary
Let us take an example:
Convert (13)₁₀  into binary
                       13/2= 6 +++   1---------------------- (carry)

 6/2= 3 +++   0 ---------------------- (carry)

 3/2= 1 +++   1----------------------- (carry)

 1/2=0 +++   1----------------------- (carry)

 So (13)₁₀ =1101₂