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Mathematics 63 Online
OpenStudy (anonymous):

Determine the representation of each of the numbers into the indicated base or notation: 27 to base two

OpenStudy (anonymous):

27 = 16 + 8 + 2 + 1

OpenStudy (anonymous):

one in the 16s place one in the 8s place zero in the 4s one in the 2s place one in the 1s place

OpenStudy (anonymous):

so \[11011\]

OpenStudy (anonymous):

I don't understand how you're getting these numbers

OpenStudy (anonymous):

you divide by powers of 2

OpenStudy (anonymous):

i started by dividing 27 by the largest power of two that goes in to it

OpenStudy (anonymous):

powers of two are 1, 2, 4, 8, 16, 32, 64, ...

OpenStudy (anonymous):

largest is 16, and 27 - 16 = 11 then 11 - 8 = 3 now 4 is larger than 3, so move on to 2 3 - 2= 1 so 27 = 16 + 8 + 2 + 1

OpenStudy (anonymous):

I'm sorry, but I'm still confused :(

OpenStudy (anonymous):

in base ten the number \(7324\) means \(7\times 10^3+3\times 10^2+2\times 10^1+4\times 10^0\)

OpenStudy (anonymous):

so you have to figure out what the largest power of 2 that goes in to 27

OpenStudy (anonymous):

ok so thats 16

OpenStudy (anonymous):

27-16=11 11-8=3 3-2=1 27=16+8+2+1 but how do you get the final answer out of that?

jimthompson5910 (jim_thompson5910):

another way to do it divide 27 by 2 to get 27/2 = 13 remainder 1 take the answer 13 and divide it by 2 to get 13/2 = 6 remainder 1 repeat and do it til you get a quotient of 0 6/2 = 3 remainder 0 repeat again 3/2 = 1 remainder 1 repeat again 1/2 = 0 remainder 1 We stop now since the quotient is 0 So now read the remainders in reverse to get 11011 so 27 base 10 = 11011 base 2

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