SOLUTION: convert each of the fallowing number to numerals in the indicated system? (a) 29 to base two (b)11011two to base ten (c)9 to base two

Question 352908: convert each of the fallowing number to numerals in the indicated system?
(a) 29 to base two
(b)11011two to base ten
(c)9 to base two
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
The key to working with different bases is to understand that every place value represents a power of the base. For base ten, the system we know best, the place values are well known: 1, 10, 100, etc. But you may not realize that these are all powers of 10:

etc.
The place values in base two will be powers of two.

etc.
So the rightmost digit in base two is the ones place in base two. (Because a zero exponent always results in 1 the rightmost digit of all>/i> bases will be the ones place!)
Proceeding to the left, the place values in base two will be
ones
twos
fours
eights
sixteens
thirty-twos
etc.

Now we are ready to answers the questions:
(a) 29 to base two
To change from base 10 to base two we have to break up the base ten number into a sum of powers of two.
29 = 16 + 8 + 4 + 1
And then replace these powers of two with their base two representation:
10000 + 1000 + 100 + 1 = 11101

(b)11011two to base ten
Here we will reverse the process. For each one in the base two number we will add in the base ten version of that place value. The first 1 is in the 16's place, the second 1 is in the 8's place, the third 1 is in the 2's place and the last 1 is in the ones place. So
11011two = 16 + 8 + 2 + 1 = 27

(c)9 to base two
Repeating the process of problem (a):
9 = 8 + 1
So in base two nine is
1000 + 1 = 1001
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