Binary to decimal conversion states the conversion of a binary number (base-2) to an equivalent decimal number (base-10). A number system is used to express numbers in mathematics. It is a way of displaying numbers. The following are the four distinct categories of number systems:
- Binary Number System (Base-2)
- Octal numbers System (Base-8)
- Decimal Number system (Base-10)
- Hexadecimal Number System (Base-16)
The number system is crucial in both computer architecture and the creation of electrical devices. As a result, learning how to convert one number system to another number system is necessary. Let’s start with a basic understanding of both number systems before moving towards binary to decimal conversion.
What is a Binary Number System?
A number that is utilized in binary systems is defined as a binary number system. It’s also known as the base-2 numeral system. It uses two separate symbols to represent numeric values: 1 (one) and 0 (zero).
What is a Decimal Number System?
The base 10 numeral system is another name for the decimal number system.
It has 10 digits, ranging from 0 to 9. The locations to the left of the decimal point denote ones, tens, hundreds, thousands, and so on in the decimal number system.
How Do You Convert Binary to Decimal?
The multiplication technique is used to convert a binary number to a decimal number. If a number with base ‘n’ is to be converted to a number with base 10, each digit of the provided number is multiplied from the Most Significant Bit (MSB) to the Least Significant Bit (LSB) while the base is reduced in power.
Steps in the Binary to Decimal Conversion
- To begin, write the binary number given and count the powers of 2 from right to left ( power’s starting from 0).
- Write each binary digit (right to left ) with the matching powers of 2 so that the first binary digit (MSB) is multiplied by the highest power of 2.
- From the previous step, add all the products.
- The required decimal number will be the final answer.
Let us understand this conversion with the help of an example
Example of Binary to Decimal Conversion:
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
Math class
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