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# Binary to Decimal Converter- How to convert binary to decimal

## Binary to Decimal

A binary number (base-2) is converted to an equivalent decimal number using the binary-to-decimal conversion formula (base-10). In mathematics, numbers are expressed using a number system. It is a way to display numerical data. The four various number systems are as follows:

• System of Binary Numbers (Base-2)
• System of octal numbers (Base-8)
• System of Decimal Numbers (Base-10)
• System of Hexadecimal Numbers (Base-16)

The number system is crucial to computer systems. The number system is used by virtually all electronic devices, not just computer architecture. Therefore, learning how to convert between different number systems is crucial. Before we talk about converting from binary to decimal, let’s first grasp both number systems.

## Binary to Decimal- Binary Number System

A number that is employed in binary systems is referred to as a binary number system. The base 2 number system is another name for it. It uses two separate symbols to represent the numerical values, essentially 1 (one) and 0 (zero).

## Binary to Decimal- Decimal Number System

The base-10 numeral system is another name for the decimal number system. Ten digits, from 0 to 9, are used. The continuous locations to the left of the decimal point in the decimal number system stand in for units, tens, hundreds, thousands, and so forth. Consequently, 10 serves as the decimal number system’s base.

## Binary to Decimal Conversion

When converting a binary number (base-2) to a decimal number, this process is known as binary to decimal conversion (base-10). Understanding binary-to-decimal conversion is crucial for applications using computer programming. Only two digits, 0 and 1, are used to represent the binary number system, whereas all ten digits, from 0 to 9, are used to represent the decimal number system. In the subsequent section, we must learn how to translate a binary number into its matching decimal number.

## How Binary to Decimal Converter Works?

We use the division method to multiply the binary integer to get its decimal equivalent. In this conversion method, each digit of the input number is multiplied from the Most Significant Bit (MSB) to the Least Significant Bit (LSB), lowering the base’s power, if a number with base n is to be turned into a number with base 10.

## Binary to Decimal Conversion Steps

• Write the specified binary number first, then count the powers of two going left to right (powers starting from 0)
• Now, from right to left, write each binary digit with the matching powers of 2, so that the first binary digit (MSB) will be multiplied by the largest power of 2.
• Add each of the items from the previous step.
• The required decimal number will be the final response.

## Binary to Decimal Converter working Formula

We will learn the basic formula, let’s study how to convert a binary number to a decimal number. The formula to convert binary to decimal is provided as, where dn represents the digits of a binary number with ‘n’ digits.

The formula for conversing binary to decimal is given below Where,

N is decimal equivalent,

b is the digit,

q is the base value

## Binary to Decimal Conversion Table

Binary
Number
Decimal
Number
Hex
Number
0 0 0
1 1 1
10 2 2
11 3 3
100 4 4
101 5 5
110 6 6
111 7 7
1000 8 8
1001 9 9
1010 10 A
1011 11 B
1100 12 C
1101 13 D
1110 14 E
1111 15 F
10000 16 10
10001 17 11
10010 18 12
10011 19 13
10100 20 14
10101 21 15
10110 22 16
10111 23 17
11000 24 18
11001 25 19
11010 26 1A
11011 27 1B
11100 28 1C
11101 29 1D
11110 30 1E
11111 31 1F
100000 32 20
1000000 64 40
10000000 128 80
100000000 256 100

## Binary to Decimal Table

The conversion chart for Binary to Decimal conversion 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

## Binary to Decimal Conversion Examples

Example: Convert 11102, from binary to decimal using the binary-to-decimal formula.

Solution: We start doing the conversion from the rightmost digit, which is ‘0’ here.
(Decimal Number)10 = (d× 20) + (d1 × 2)+ (d2 × 2)+ ….. (dn-1 × 2n-1),
= (0 × 20) + (1 × 21) + (1 × 22) + (1 × 23)

= (0 × 20) + (1 × 21) + (1 × 22) + (1 × 23)
= 0 + 2 + 4 + 8
= 14
Therefore, 11102 = 1410

Example: Convert the binary number 1001 to a decimal number.

Solution: Given, binary number = 10012

Hence, using the binary-to-decimal conversion formula, we have:

10012 = (1 × 2³) + (0 × 2²) + (0 × 2¹) + (1 × 2⁰)

= 8 + 0 + 0 + 1

= (9)₁₀

Example: Convert 11010012 into an equivalent decimal number.

Solution: Using binary to decimal conversion method, we get;

(1101001)₂ = (1 × 2⁶) + (1 × 2⁵) + (0 × 2⁴) + (1 × 2³) + (0 × 2²) + (0 × 2¹) + (1 × 2⁰)

= 64 + 32 + 0 + 8 + 0 + 0 + 1

= (105)₁₀

## 1111 Binary to Decimal

1111 is in binary to decimal conversion is equal to 15.

 1111 15

## 1001 Binary to Decimal Conversion

In The binary conversion of 1001 means the 1 and the 8 bits are activated, but not the 2 or 4 bits. Thus, the binary-to-decimal conversion for 1001 is 8 + 1 = 9.

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## FAQs

### How do I convert binary to decimal?

To convert a binary number to decimal we need to perform a multiplication operation on each digit of a binary number from right to left with powers of 2 starting from 0 and add each result to get the decimal number of it.

### What is the 1111 binary to decimal?

15 is the decimal equivalent of the binary number 1111.

### How do you write 0.75 in binary?

The decimal number 0.75 is written as 0.11 in binary.

### What is 15 in binary form?

The binary equivalent of 15 is 1111.