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Convert Into Decimal Number

Complement of a Number   Number System   Types of Number system

      In our previous article, we had discussed about different types of Number System. Now, In this article we can easily understand how to convert Any Number in to Decimal Number System.

Convert Binary to Decimal – we convert binary to decimal by multiplying increasing power of two through right to left from decimal. If there is no decimal, we should start from the last digit and multiplying by increasing power of 2 up to first digit. If decimal occurs, then start from the first digit and multiply by decreasing power of 2 up to the last digit. Let’s understand with an example.

Ex 1. (110111)2

Sol. (1*25) + (1*24) + (0*23) + (1*22) + (1*21) + (1*20)

        (1*32) + (1*16) + (0*8) + (1*4) + (1*2) + (1*1)

        32 + 16 + 0 + 4 + 2 + 1

        (55)10                   Ans.

Ex 2. (1001.01)2

Sol. (1*23) + (0*22) + (0*21) + (1*20) + (0*2-1) + (1*2-2)

        (1*8) + (0*4) + (0*2) + (1*1) + (0*0.5) + (2*0.25)

        8 + 0 + 0 + 1 + 0 + 0.50

        (9.50)10              Ans.

Note: If Binary Number contains decimal point then after decimal point we have to start multiply by 2-1 not 20 and so on.

Convert Octal To Decimal – This also works in the same way, only difference is that we should multiply by 8 in place of 2. Because the base of octal is 8. Let’s understand with an example.

Ex 3. (763.4)8

Sol. (7*82) + (7*81) + (7*80) + (4*8-1)

        (7*64) + (7*8) + (7*1) + (7*0.125)

        448 + 56 + 7 + 0.875

        (511.875)10                           Ans.

Convert Hexadecimal To Decimal – This also works in the same way, only difference is that we should multiply by 8 in place of 2. Because the base of hexadecimal is 16. Let’s understand with an example.

Ex 4. (B65F)16

Sol. (11*163) + (6*162) + (5*161) + (15*160)

        (11* 4096) + (6*256) + (5*16) + (15*1)

        45056 + 1536 + 80 + 15

     (46687)10             Ans.

Note: In Ex 4. Here we use some alphabets as well as digits because hexadecimal has a base 16 and it takes digits through 0 to 9 and alphabets through A to F. So it takes total 10 digits and 6 alphabets in hexadecimal Number System. If you don’t understand how to take alphabets as well as digits in Ex 4. Don’t worry we will describe in detail in upcoming articles.

Trick: Any Number which you want to convert into decimal, multiply by it with its corresponding base as we had already seen in above examples.

Exercise:

Convert the following Number in to Decimal

1.       (00101.11)2

2.       (1111.11)2

3.       (421.21)5

4.       (7633.54)8

5.       (B6A54)16

 

 

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