CONVERSION FROM BINARY TO VARIOUS NUMBER SYSTEM

Number Systems in Digital Electronics
Number Systems in Digital Electronics

CONVERSION FROM BINARY TO VARIOUS NUMBER SYSTEM.

In the previous article we covered the basics of number system used in digital electronics. In this article we will cover the conversion of one number system to another. If you are not aware about the number system visit this link “Introduction”

Basics:

There are various ways to represent number but the most common ways used in digital system are Decimal, Binary, Octal and Hexadecimal. Each number system can be converted to another by following step wise procedure which we are going to cover in this article.

CONVERSION FROM BINARY TO DECIMAL :

Decimal number is obtained by adding the powers of 2 of binary number. The power of 2 is determined by position of digit, the power goes on increasing while moving towards left and goes on decreasing by moving towards right.

FOR EXAMPLE : Convert binary number 1011.11 into decimal.

SOLUTION : First use step 1 and 2

=  1  0  1  1  .  1  1

= 1*2^3 + 0*2^2 + 1*2^1 + 1*2^0  + 1*2^-1 + 1*2^-2

Now Step 3  :  8+0+2+1+0.5+0.25 = 11.75

Hence  (1011.11)  2 = (11.75) 10

CONVERSION FROM BINARY TO OCTAL :

BINARY                                             OCTAL

000                                                        0

001                                                        1

010                                                        2

011                                                        3

100                                                        4

101                                                        5

110                                                        6

111                                                        7

STEPS TO BE FOLLOWED :

  • Note down the given binary number and split it into group of 3 starting from LSB.
  • Now refer the table given above and convert each group into corresponding octal number.

FOR EXAMPLE : Convert binary number (110010)2  to octal.

SOLUTION : First use the step 1

= 1 1 0 0 1 0

=   1 1 0                                           010

GROUP 2                                  GROUP1

Step2

6                                                 2

Hence (110010)2 = (62)8.

CONVERSION FROM BINARY TO HEXADECIMAL :

 

CONVERSION FROM TO VARIOUS NUMBER SYSTEM
CONVERSION FROM TO VARIOUS NUMBER SYSTEM

STEPS TO BE FOLLOWED :

1)    Note down the given binary number and split it into group of 4 starting from LSB.

2)    Now refer table given above and convert each group into corresponding hex number.

FOR EXAMPLE : Convert (10101111)2  to hexadecimal.

SOLUTION : First use step 1.

= 1  0  1  0  1  1  1  1

=1 0 1 0               1 1 1 1

Step 2  :           A                           F

Hence (10101111)2 = (AF)16 .

 

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