conversions

Ok people let’s do it ONE more time….as far as conversions are concerned u have to remember this

1)      Why do we need to convert the numbers in the first place?

Answer: Computers CANNOT understand our language….being a machine they only understand the concept of ON(1) and OFF(0). Hence 0 and 1. All the numbers in binary language are made of only these two numbers. For example 0,1,10,11,100,101,111……..

2)      What are decimal numbers then?

Answer: These are the numbers that we use in our daily life they range from 0-9. Hence 0.1,2,3,4,5,6,7,8,9. 

3)      Why do we have the decimal number system in the first place?

Answer: with more numbers, representation becomes easier to understand…if there were just binary numbers in the world it would have been difficult understanding them

For example if I ask you 11101001000 and 1100100100010 or 111111110001011000111001 you will be  :o  and it would be difficult to understand them.

Also since humans have ten fingers we have ten numbers J

4)      How do we convert binary to decimal?

Answer: easy as a pie…multiply each digit with 2 and start giving power in ascending order (starting from 0) and add the individual results

For example:

1012

= 1 x 22 + 0 x 21 + 1 x 20 

=1x 4 + 0 x 2 + 1 x 1

=4+0+1

=510

5)      How do we convert from decimal to binary?

Answer:  Again piece of cake…remember LCMS? Sure u do….the same thing but with only the number 2 ! and yaa…obvs every number is not divisible by2 so look at the remainders and read the remainders bottoms up

       

Hence the number is 1012

6)      Sir, why did you make us do the conversions from other bases when they are not on the syllabus?

Answer:  it’s fun being sadistic >:) actually no. the reason was that so you know the concept NOT the formulae !

7)      How do we convert from other bases?

Answer:  exactly the same way as you did previously…multiply each digit of the number with the base written on the lower right

for example

157

=1 x 71 + 5 x 70

=1x 7 + 5 x 1

= 7 + 5

= 1210

8)      How about back from decimal to ANY other base?

Answer:  Exact same manner…take LCM with that base…from example

Convert

1510 to base7

Hence the number is 217