How to Convert Binary to Decimal

It is important to convert Binary to Decimal system as it is important for computer and digital systems. In the decimal numbering system, a base of 10 is used. In this, each digit will take one value from 0 to 9.

These also have basic mathematical operations:

  • Addition
  • Subtraction
  • Division
  • Multiplication

Also, Check: Binary to Decimal Calculator

In a decimal system

  • Every digit will have the value 10 times more than the last number
  • This system uses a set of few symbols b, q to find the weight of every digit in the given number. Here q is the base
  • Example – Let’s assume two numbers 50 and 500, here 5 in 50 has less weightage than 5 in 500

Binary to Decimal converter

To convert Binary to Decimal, we use multiplication method. If the number has a base of n which is to be converted into another number of base 10 then we need to multiply MSB to LSB by reducing the base power. Similarly binary to decimal can be converted by using another formula.

Binary to Decimal Example Problems

1. Convert (1101)2 into decimal number.

Solution: The given binary number is (1101)2

Now, multiplying each digit from MSB to LSB with reducing the power of the base number 2.

1 × 23 + 1 × 22 + 0 × 21 + 1 × 20

= 8 + 4 + 0 + 1

= 13

So, (1101)2 = (13)10

Binary to Decimal Formula

Binary to Decimal Formula

Where,

N is decimal equivalent,

b is the digit,

q is the base value

Binary to Decimal chart

Binary

Decimal

0

0

1

1

10

2

11

3

100

4

101

5

110

6

111

7

1000

8

1001

9

1010

10

1011

11

1100

12