Question

How to convert the decimal number 0.0625 to binary?

Answer 1

in decimal notation, the number 0.0625 is really

0.0625 = 0*10^(-1) + 6*10^(-2) + 2*10^(-3) + 5*10^(-3)

Answer 2

notice we have the the digits of 0.0625 circled

Answer 3

the 0 after the decimal place is in the 10ths place

so that is why I multiplied by 10^(-1) = 1/10

6 is in the hundredths place, which is why I multiplied by 10^(-2) = 1/10^2 = 100

etc etc

Answer 4

making sense?

Answer 5

Yeah, I know all conversion ways except going from a decimal fraction to binary.

Answer 6

oh wait, nvm, I'm thinking in reverse

this page however has a good method to convert from decimal to binary (including fractional decimals)

http://cs.furman.edu/digitaldomain/more/ch6/dec_frac_to_bin.htm

Answer 7

Sweet, any other method I've seen so far was too convoluted. This one is nice and simple.
Thanks.

Answer 8

what answer do you get when you convert 0.0625 base 10 to base 2?

Answer 9

0.0001

Answer 10

I got 0.0001 base 2 as well

and notice how

0.0001 base 2 = 0*2^(-1) + 0*2^(-2) + 0*2^(-3) + 1*2^(-4) base 10

0.0001 base 2 = 0*(1/2) + 0*(1/4) + 0*(1/8) + 1*(1/16) base 10

0.0001 base 2 = 1/16 base 10

0.0001 base 2 = 0.0625 base 10