Binary to Decimal Conversion examples

Binary Number System

In binary number System, the number are in the form of (0, 1).
0 for Low and 1 for High .
The Symbol 0, 1 Known as bits.

The Format used in binary number system is

..... 2³2²2¹2⁰· 2^-1 2^-2 2^-3 …….

2⁰= 1

2¹= 2

2²= 4

2³= 8

or in simple form it is ..... 8, 4, 2, 1 · 0.5, 0.25, 0.125…….

Binary to Decimal conversion

Example 1. Convert the binary number (1 1 0 1 0 1)₂to decimal.

Sol. Just apply the format of binary no. to the number which have value 1 and simply add it

Now Add the number to get the result.

32 + 16 + 4 + 1 = 53

so the Binary conversion of (1 1 0 1 0 1)₂ to Decimal is 53.
Note: binary value (1 1 0 1 0 1)₂ has a base 2 because it represents the number is in binary form.

Example 2. Convert the fractional binary number (0.1011)₂ into decimal.

Sol. First Determine the weight of each bit and then sum the weights times the bit.

Now Add the number to get the result.

0.5 + 0.125 + 0.0625 = 0.6875

so the Binary conversion of (0.1011)₂ to decimal is 0.6875.

Note: binary value (0.1011)₂ has a base 2 because it represents the number is in binary form.

Decimal to Binary conversion

Easy Method to Find Binary to Equivalent is as follows .
For Example : 9 is convert to binary.
so 8 + 1 = 9
By using Binary format i.e., ( 8 4 2 1). We can convert 9 decimal into binary.

Just put 1 below the number by which we can get 9 by adding those number and 0 to others.