Binary to Decimal Conversion

In Mathematics, a number system is used for expressing numbers. It is a way to represent the numbers. The four different types of number system are:

  • Binary Number System (Base 2)
  • Octal Number System (Base 8)
  • Decimal Number System (Base 10)
  • Hexadecimal Number System (Base 16)

Number system plays an essential role in computer architecture. Not only computer architecture but mostly all electronic gadgets also uses the number system. So it is essential to learn the conversion from one number system to the other number system. In this article, we are going to discuss binary to decimal conversion, formula, and examples.

What is a Binary Number System?

A binary number system is defined as a number that is used in the binary systems. It is also called base 2 numeral system. It represents the numeric values with two distinct symbols, basically 1 (one) and 0 (zero).

What is a Decimal Number System?

The decimal number system is also known as the base 10 numeral system. It uses ten digits from 0 to 9. In the decimal number system, the positions continuous to the left of the decimal point represent units, tens, hundreds, thousands and so on. Thus, the base of the decimal number system is 10.

Also, Check: Binary to Decimal Calculator

How to Convert Binary to Decimal Numbers?

To convert the binary number to a decimal number, we use the multiplication method. In this conversion process, if a number with base n has to be converted into a number with base 10, then each digit of the given number is multiplied from the Most Significant Bit (MSB) to the Least Significant Bit (LSB) with reducing the power of the base. Let us understand this conversion with the help of an example.

Example of Binary to Decimal Conversion:

Convert the binary number (1101)2 into a decimal number.

Solution:

Given binary number = (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

Thus, the equivalent decimal number for the given binary number (1101)2 is (13)10

Binary to Decimal Conversion Formula

The formula for the conversion of the binary number to the decimal number is given by:

Binary to Decimal Formula

Where,

N is decimal equivalent,

b is the digit,

q is the base value

Binary to Decimal Conversion Chart

The conversion chart for the binary to the decimal number is given below.

 

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

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