Binary To Decimal Conversion: Conversion Formula And Chart

Binary to Decimal Conversion: The Binary number system has its roots in multiple ancient cultures such as Egypt, India and China, but it came to be the internal language of electronic computers later on. On the other hand, the decimal numerical system is a base-10 system as opposed to binary, which is a base-2 numerical system. Since both the number systems are prominently in use, it is crucial to know how to convert binary numbers to decimals.

However, students have to be careful not to mix up the two sets of numbers while binary to decimal conversion. There are four various types of Number Systems are-

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

Go down to the article, to get a detailed explanation with the example of Binary to Decimal Conversion.

Binary To Decimal Conversion

For clarification know the definition for both Binary and Decimal numbers we have given below:

Binary Numbers

A binary number system is described as a number, which is used in binary systems. It is also known as the base 2 numeral system. It interprets the numeric values with two distinguished symbols, basically 0 (zero) and 1 (one).

Decimal Numbers

The decimal number system is also called the base 10 (ten) numeral system. It uses ten digits from zero to nine (0 to 9). In the decimal number system, the positions connected to the left of the decimal point signify units, tens, hundreds, thousands, etc. Therefore, the base of the decimal number system is 10 (ten).

How To Convert Binary To Decimal?

In binary to decimal conversion, students have to use the multiplication method. In this conversion process, if a number with base ‘n’ has to be converted into the number with base 10, then each digit of the provided number is multiplied by the MSB (Most Significant Bit) over the LSB (Least Significant Bit) with reducing the power of the base. Let’s understand this through the example.

Example- Convert the binary number $${(1101)_2}$$ into a decimal number.

Solution- Given binary number = $${(1101)_2}$$

Multiply each digit from MSB to LSB with reducing the power of the base number 2.

$$1 \times {2^3} + 1 \times {2^2} + 0 \times {2^1} + 1 \times {2^0}$$

= 8 + 4 + 0 + 1

= 13

So, the similar decimal number for the given binary number $${(1101)_2}$$ is $${(13)_{10}}$$.

Binary to Decimal Conversion Formula

The formula to convert the binary number to the decimal number is mentioned below-

Decimal Number =

$$DecimalNumber = {n^{th}}bit \times {2^{n – 1}}$$

Binary to Decimal Formula,

$$n = {b_n}{q^n} + {b_{n – 1}}{q^{n – 2}} + ….. + {b_2}{q^2} + {b_1}{q^1} + {b_0}{q^0} + {b_{ – 1}}{q^{ – 1}} + {b_{ – 2}}{q^{ – 2}}$$

Where,

n- decimal equivalent

b- digit,

q- base value

Chart of Binary to Decimal Conversion

Know a few of the conversion of binary to decimal in the following table for reference:

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

FAQs On How To Convert Binary To Decimal?

Ques 1- What does 101 mean in binary?
Ans-101 in binary means 4 + 1 = 5 because the first ‘1’ is in the “fours” column, and the second ‘1’ is in the “ones” column.

Ques 2- How do you calculate binary?
Ans- To calculate the numerical value of a binary number, sum up the value for each position of all the ones in the eight-character number. The number 01000001, for example, is converted to 64 + 1 or 65.

Ques 3- What is the short name of binary math?
Ans- In maths and digital electronics, a binary number is a number represented in the base 2 numeral system or binary numeral system, which applies only two symbols typically- “0” (zero) and “1” (one).
The base 2 numeral system is a positional representation with a radix of 2. Each digit is indicated as a bit or binary number.

Ques 4- Is binary infinite?
Ans- Yes – the only binary numbers that have a finite number of digits can be represented accurately by the sum of negative powers of 2. for instance, both cannot be defined precisely by binary decimals; there are infinitely more.

Ques 5- Can all fractions be represented in binary?
Ans- The binary numbering system is a base-2 numbering system that contains only two digits, a “0” or a “1”. Compared to decimal fractions, binary numbers can also be interpreted as unsigned fractional numbers by setting the binary digits to the right side of the binary point or decimal point.

The main benefit of binary coded decimal is that it provides easy conversion between binary (base-2) and decimal (base-10) forms. The disadvantage is that the BCD code is destructive as the states between 1010 (decimal 10) and 1111 (decimal 15) are not used.

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