We use Number Systems everywhere. With increasing influence of computer systems in our everyday tasks, conversion of Decimal to Binary and Binary to Decimal Number system has become must. In this post, we will try to understand What is Computer Number System, Decimal Number System, Binary Number System and most importantly conversion from Decimal to Binary and Binary to Decimal numbers.

Table of Contents

## What is Computer Number System

The mastery over depiction & symbolization of the numbers through performing certain conversion tasks on them to make then equivalent is called Number System. This forms the fundamentals of Computers Number system. Computers recognize and converts common man’s stereotyping of words and letters into numbers. There are mainly four different groups of Number Systems:

- Decimal System
- Binary System
- Octal System
- Hexadecimal System

## Decimal Number System

Decimal number system is used in our everyday business. Normally in this genre of rendition non-identical positions are given to each numeral connoting the number depending upon their setting points.

The units, tens, hundreds, thousands and so on of the decimal number system take consecutive places to the left of the decimal point to exemplify it. The decimal number system appoints 10 as its plinth/ base and it houses the 10 diverging numerals, the digits are 0,1,2,3,4,5,6,7,8,9.

What if there are more digits than the single digits? Place value notation (weighing factor) is the solution for us to further represent the numbers in powers of 10 as each of the subsequent digits is associated with the weighing factor.

**Example 1**: How to Represent Integer Number

We will learn how to represent 84531 which is an integer number.

**Example 2**: How to Represent Real Number

Decimal number system depends upon a decimal point to reproduce decimal fractions. We will learn how to represent 52.364 which has decimal point and is a real number.

We read .364 as ‘Point 3, 6, 4’ as it is conducive to spell the number this way. The decimal point dichotomizes the whole number part from the fractional part of a number.

## Binary Number System

The Binary Number system uses base-2 system to outline and elucidate its binary numbers and its profound uses are in the areas of Mathematics and Digital electronics. It traces out only two regalia typically **0 (Zero)** and

**1**.

*(**One*)

The Binary Numeral system has a rhizome of 2 with a positional notation. Binary digits are called bits and these bits hold no implication by themselves if they are not harmonized together.

Computer systems avail Binary Number system because it has an edge over other number systems since the usage here is limited to just two symbols ‘0 and 1’ and this is the only cardinal language that makes the computers apprehend 0 as ‘Off’ and 1 as ‘On’.

Binary Numbers use powers of ** (2^{n})** by efficaciously augmenting the value of each subsequent binary digit as it moves forward from right to left and it doubles for each movement.

For example – 1, 2, 4, 8, 16, 32, etc.

There are primitive forms of Binary numbers:

- A Bit – Single binary digit
- A Nibble – 4 binary digits
- A Byte – 8 binary digits
- A Word – 16 binary digits

### Example : How Do We Represent Binary Numbers

As discussed above, a Binary number is always represented using ‘0 and 1’. While reading it, each digit is read separately. Lets understand it with an example. If we have to read the Binary number (110.10)_{2} , we should read it as ‘One One Zero Point One Zero’.

## Conversion from Decimal to Binary Number System

For ease of understanding, we will try to learn it with some examples.

**Example 1**: How to Convert Simple Number Without Decimal to Binary

We will understand how to convert Decimal number 458 into it Binary equivalent.

For conversion from Decimal to Binary, we have to continuously divide the decimal number by 2 until the remainder becomes 0 or 1 .

Then congregate all the remainders starting from the **Least Significant Bit (LSB)** from the antipodal region all the way till we reach the top of the number that is **Most Significant Bit (MSB)** and this forms the deserved Binary number.

So, the result will be (458)_{10} = (111001010)_{2}

### Example 2: How to Convert Simple Number With Decimal to Binary

We will understand how do we convert a decimal number if there is decimal point involved in it. Lets take 458.692

It works the same way as above to deduce the binary number for the given decimal number for the integer part that is the number, which is towards the left side of the decimal point or before the decimal point.

For the number that is after the decimal point or the towards the right side of the decimal point, start multiplying the fractional part including decimal point by 2 until the first digit after decimal point becomes 0.

Here gathering the numbers is done from top Most significant bit (MSB) to **Least significant bit (LSB)** below unlike its counterpart.

So, the final result will be (458.692)_{10}_{ = }(111001010.1011)_{2}

## Conversion from Binary to Decimal Number System

Let’s take some examples to understand Binary to Decimal conversion in a better way.

**Example 1**: How to Convert Binary Number Without Decimal Point to Decimal

We will understand how to convert a Binary to Decimal equivalent. So let’s take a number (1110)_{2}

Each Binary digit is multiplied by 2n depending upon its weighing factor and later all the numbers are added (sum of weights) to form a Decimal number.

So, the final result will be (1110)_{2} = (14)_{10}

**Example 2**: How to Convert Binary Number With Decimal Point to Decimal

Lets take (1110.011)_{2 } for example .

In this case, the binary digits before the decimal point will be converted as explained above.

For the binary digits which are after the decimal point, each digit will be multiplied by a fraction of 1/2n in the increasing format from the left digit after the decimal point to the right most digit. After that, sum of weights will be performed to get the final decimal number.

So, the final result will be (1110.011)_{ 2} = (14.375)_{ 10}

**Note** : The conversion systems make use of subscript (x_{2}) to mainly denote which number systems are in usage and what conversions are taking place and superscript (x^{2}) to show the numbers given have been raised to some powers to show the weighing factor.

Author: Savitha Rishank Chegu

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