What is Decimal Number System Full Details

What is Decimal Number System

In digital electronics or in computers, the number system is used to give information to a computer. There are many types of number systems. Such as- Decimal Number System, Binary Number System, Octal Number System, Hexadecimal Number System.

The base of the decimal number system is base 10. We also call it subscript or radix. Numbers in the decimal number system range from 0 to 9, i.e. 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

In the Decimal Number System, the numbers (Digits) are written something like this, (32)10

If you look at the first number written on your right hand side then it is called LSB (Least Significant Bit). The first number written on the reverse hand side is called the MSB (Most Significant Bit). Look at the example given below,

Example- (56893)10

Decimal number system

Hope you guys have understood what is MSB and LSB?

If we want to write the number 56893 in maths, can someone tell me how we can write it?

Some will write in this way, 50000 + 6000 + 800 + 90 + 3. Now if I want to write them to the power of 10 (power of 10) then how will I write it? Some would write as 5 × 104 + 6 × 103 + 8 × 102 + 9 × 101 + 3 × 100. This is why I told that 10 to the power of 4 or 10 to the power of 3, we call these powers as weights. And when we do decimal conversion or convert decimal to binary, then it is important for us to have knowledge of them.

How to Convert Decimal to Binary Number System

Decimal number ko binary number me kaise badle? Let us understand, 7 which is a decimal value, how to convert it to binary? To get the value in binary, divide 7 by the base 2 of the binary, and write the remainder at one place. sorts of,

To convert any decimal number to binary, divide the decimal number by 2. Divide the obtained quotient by 2 until the quotient is zero.

Remainder is written from bottom to top, as shown in the above figure.

(7)10 = (111)2

Example- Convert Decimal number 56 to binary. (56)10 = (?)2

How to Convert Decimal to Octal Number System

For Decimal number ko Octal me badalne, divide the decimal number by the base (8) of the octal number.

Question- Convert the decimal number given below to octal.

(123)10 = (?)8

answer-

(123)10 = (173)8

How to Convert Decimal to Hexadecimal Number System

For Decimal ko Hexadecimal me badalne, divide the decimal number by the base (16) of the hexadecimal number.

Question- Convert 123 which is a decimal number to hexadecimal.

answer-

As we know 11 = B in hexadecimal, so the output will be = (7B)16

Binary to Decimal Conversion

Let us understand with an example how to convert binary to decimal. We know that the base of a binary number is 2.

Example- (101011)2 = (?)10

Start counting the number from your right hand side. Something like this,

Now write to the power of 2 and multiply the digit together. Something like this (start writing from the right hand side),

= 1 × 20 + 1 × 21 + 0 × 22 + 1 × 23 + 0 × 24 + 1 × 25

= 1 + 2 + 0 + 8 + 0 + 32

= (43)10

Octal to Decimal Conversion

Example- (47)8 = (?)10

The process of solving this question is exactly like the one solved above,

= 7 × 80 + 4 × 81

= 7 × 1 + 4 × 8

= 7 + 32

(47)8 = (39)10

Hexadecimal to Decimal Conversion

We can understand with an example how to convert any hexadecimal number to decimal. Understand the example given below,

Example- (F A 9 2)16 = (?)10

answer-

= 2 × 160 + 9 × 161 + A × 162 + F × 163

= 2 + 144 + A × 256 + F × 4096

We know that in Hexadecimal Number System A = 10 and F = 15,

= 2 + 144 + 10 × 256 + 15 × 4096

(F A 9 2)16 = (64146)10

Conclusion

To convert any number from one form to another, it is necessary that you know what is the base of Decimal Number, Octal Number, Binary Number and Hexadecimal Number? Also, it should also be known that how many digits come in which system number. For example, the numbers from 0 to 9 come in the decimal number. Write below two tips, hope it will help you,

Tip 1- Whenever converting a decimal number to octal, binary or hexadecimal, keep in mind that always divide the decimal number by the base of octal, binary and hexadecimal.

Tip 2- If you are converting to octal, binary and hexadecimal numbers, always multiply the octal, binary and hexadecimal base by each digit and its power (3 × 80 ).

I hope you have understood well what is Decimal Number System.

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