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Binary to Decimal Conversion

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Last updated date: 16th Jul 2024
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Binary to Decimal Conversion in Detail

Mathematics can be said to be a collection of different number systems, which are used to represent and express numbers. In total, there are four types of number systems in mathematics. These numbers systems vary as per the number of ‘base’ they use. Base or radix can be said to be a combination of digits which helps represent a number. In the order of increasing count of bases, their names are as follows:

  • Binary system (Base of 2).

  • Octal System (Base of 8).

  • Decimal System (Base of 10).

  • Hexadecimal System (Base of 16).

Number system and its application have a major role to play in computer science. One system might not fulfil every purpose or task. Thus, the conversion of one number system to another number system is equally essential. For example, we might need to convert binary number to decimal number, and vice versa when required.

To master number system conversion, students first need to be thorough with each system, their bases, representation, and so on. Here you will learn how to convert a binary number to decimal. Understand the two systems thoroughly first before proceeding to the conversion.

Binary Number System

Binary number system can be said to be the simplest one in the number system. It uses only two digits (0 and 1) to represent a number. Thus, as the ‘bi’ in its name suggests, the system uses 2 as a base. The entire number system can be represented through the binary system. For example, fractions, real numbers, as well as large numbers, can be represented through binary numbers.

This system is mostly used in networking, communication, electronic devices and computers. Binary numbers are also called bits. Numbers like 1011, 1101, and 1100 are binary numbers or bits.

Decimal Number

Decimal numbers are expressed with the base of 10 (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9). Such numbers have two parts. They are:

  • Whole number part.

  • Decimal or fractional part.

The two parts in a decimal number are separated by a point, or dot called the decimal point. All the digits lying on the left of this point represents the whole number. On the other hand, digits lying on the right of this point represent the decimal part.

For example, 45.4 is a decimal number. Here, 45 represent the whole number, while 5 represent the fractional part.

Now, you can proceed to understand how to convert binary to decimal. Students must also make sure to follow the examples and solve plenty of sums to understand the conversion thoroughly.

How to Convert Binary Number to Decimal Number?

The method used to find the decimal equivalent of the binary number and the binary equivalent of a decimal number is called the multiplication method. You are likely to come across two terms while going through the binary to decimal conversion steps. They are MSB (Most Significant Bit) and LSB (Lease Significant Bit). The term ‘bit’ signifies a binary number.

In a binary number, MSB is the bit lying furthest to the left while LSB is the bit lying furthest to the right. Now, have a look at how the binary number to decimal conversion is done:

Here, we will convert the bit 1100 into a decimal number. To get the decimal equivalent, we will have to consider (1100)2. Each digit starting from MSB till LSB is to be multiplied with the reducing power of base number 2:

1 × 23 + 1 × 2+ 0 × 21 + 0 × 20

This equation gives 8 + 4 + 0 + 0 = 12. Thus, the decimal equivalent of binary number 1100 is 12.

Similarly, if you are asked to convert 1010 binary to decimal, the equation would be:

1 × 23 + 0 × 2+ 1 × 21 + 0 × 2

= 8 + 0 + 2 + 0. Thus, the decimal equivalent, in this case, is 10.

The formula which coverts binary number to decimal to give the required equivalent is:

Decimal number = nth bit x 2n-1

To understand the implications of this formula, go through the examples and sums thoroughly.

Students learning binary number to decimal number conversion can take help of the Vedantu App. The lesson PDFs provide thorough guidance on each Mathematics chapter. This is backed with examples, solutions, sample papers, and so on. Moreover, the platform has expert teachers who are always there to address the doubts of a student.

FAQs on Binary to Decimal Conversion

1. How is Decimal Number Different from Binary Numbers?

Ans. Binary numbers are represented in the base of 2 (0 and 1) while decimal numbers are represented in the base of 10 (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9). Binary numbers are constituted either by 1 or 0. Decimal numbers carry two parts. One of which is the whole number and the other is a fractional part. These two parts are separated by a point or dot in a decimal number.

2. What is the Decimal Equivalent of 1100?

Ans. To find the decimal equivalent of the binary number or bit 1100, we will have to implement the multiplication method. Breakdown of this method gives 1 × 23 + 1 × 22 + 0 × 21 + 0 × 20. This equation gives 8 + 4 + 0 + 0 = 12. Thus, the decimal equivalent of 1100 is 12.

3. What is the Formula to Convert Binary Number to Decimal?

Ans. The formula used in the multiplication method of converting a binary number to decimal number is nth bit x 2n-1. Here the MSB and LSB are multiplied with the reducing base power.