Introduction: Convert Fractional Decimal to Binary Using Calculator!!!

By Adithya T G
About: Passionate about Electronics and Communication Engineering, IOT, Microcontrollers.

We will Learn how to Convert Fractional Decimal to Any Other Number System!

Intro:

1) Decimal Number System:

Use numbers : 0,1,2,3,4,5,6,7,8,9

Represented as Base10

2) Binary Number System :

Use numbers: 0,1

Represented as Base2

3) Octal Number System:

Use Numbers: 0,1,2,3,4,5,6,7

Represented as Base8

For Example :

Lets Calculate:

(95.677)base10 == (???) base 2

with 6 precision digits after decimal point in the answer?

We can use Calculator to find the answer. But the problem is that the calculator wont accept decimal points during conversion ( ie.. it only accepts 95 but not 95.677)

to overcome this there is a trick we can use!!!

Trick is to convert the number to a "big" number by multiplying it and then convert back to required number by dividing with same number. We will see this in 3 simple steps.

Step 1: Making Numerator and Denominator Ready

we know that if we multiply and divide any number by same number then the value of number wont change!

for example : 5 = (5 *10) / 10

now applying same principle we multiply the divide the original number by base of the system to which we have to convert, raised by power of precision required.

round off the numerator to nearest integer.

Step 2: Converting the Numerator to Big Number

Next Convert the numerator to required number system . Keep the denominator as is it

Step 3: Getting Final Answer!

We know that if we divide any number by its base number we shift the decimal place by left by one place.

for example : 5478 be a decimal number , therefore its base is 10 (base10)

5478/10 = 547.8

5478/(10^2) = 54.78

5478/(10^3) = 5.478 and so on...

similarly we have (101001)/ 2^2 will be 1010.01

there apply same principle to step 2 (denominator is base ^ precision ) to get the required final answer .

Step 4: Final Answer!!

Hence the final answer is

(95.677) base10 = (1011111.101011) base2

This Technique can be used to convert from any number system to any other number system of your choice involving fractions!!!!!

This is particularly useful for Engineering Math Problems!

Have a Nice Day!