A binary number is most preferred in modern computer engineers, networking and communication specialists, and other professionals. There are two ways to convert a binary number into a decimal number. Here is how you can convert binary to decimal.
The decimal number is equal to the sum of binary digits (dn) times their power of 2 (2n):
Decimal = d0×20 + d1×21 + d2×22 + …
Using Positional Notation
- Write down the binary number and list the powers of 2 from right to left.
- Multiply the positional value of binary with their digit and get the sum of these steps.
Example:
Find the decimal value of 1110012:
Binary Number | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 1 |
---|---|---|---|---|---|---|---|---|
Power of 2 | 27 | 26 | 25 | 24 | 23 | 22 | 21 | 20 |
100111012 = 1⋅27+0⋅26+0⋅25+1⋅24+1⋅23+1⋅22+0⋅21+1⋅20
= 128+0+0+16+8+4+0+1
= 15710
Using Doubling
This is a simple method to convert a binary number into a decimal number.
- Write down the binary number.
- Starting from the left, double your previous total and add the current digit.
- Double your current total and add the next leftmost digit.
- Continue doubling your current total and adding the next digit until you’ve run out of digits.
Example:
11101110 2 = (238)10
0 x 2 + 1 = 1
1 x 2 + 1 = 3
3 x 2 + 1 = 7
7 x 2 + 0 = 14
14 x 2 + 1 = 29
29 x 2 + 1 = 59
59 x 2 + 1 = 119
119 x 2 + 0 = 238
This post was last modified on August 24, 2020 11:10 pm