Question 1190037
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The other tutors have great answers. Here's an alternative approach


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Part (a)


We'll need the powers of 2
1,2,4,8,16,32,...


Start with 15. Then subtract off the largest possible power of 2. In this case, we can subtract off 8
15-8 = 7
Then subtract off 4
7-4 = 3
Subtract off 2
3-2 = 1
Then subtract off 1
1-1 = 0


Work that process in reverse and we get
15 = 1+2+4+8
Showing that
15 base 10 = <font color=red>1111 base 2</font>
Each '1' is like a lightswitch that turns on the powers of 2 we're summing. 



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Part (b)


We could use the previous idea but here's another way


15 base 10 = 1111 base 2
2 base 10 = 0010 base 2


13 base 10 = (15 base 10) - (2 base 10)
13 base 10 = (1111 base 2) - (0010 base 10)
13 base 10 = 1101 base 2


210 base 10 = 208 base 10 + 2 base 10
210 base 10 = (16*13) base 10 + 2 base 10
210 base 10 = 1101 0000 base 2 + 10 base 2 ... see note below
210 base 10 = <font color=red>1101 0010 base 2</font>


note: multiplying by 16 in base 2 is as easy as sticking four zeros at the far right end of the number
It's not a coincidence that 2^4 = 16.


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Part (c)


Like with part (b), I'll try to break this number into parts of 16. Or at least, try to get close to such multiples of 16.


As Alan alluded to, it's probably better to work with hexadecimal (base 16) since the numbers in binary are very long strings of 1's and 0's. It's easy to get lost.


7 base 10 = 0111 base 2


119 base 10 = 112 base 10 + 7 base 10
119 base 10 = (16*7) base 10 + 7 base 10
119 base 10 = 0111 0000 base 2 + 0111 base 2
119 base 10 = <font color=red>0111 0111 base 2</font>


If you are more familiar with the other methods presented by the other tutors, then ignore my post entirely. 


I recommend the use of any online calculators that quickly convert from binary to decimal (and vice versa) to check your work. Keep in mind that it's not a good idea to rely entirely on the calculator because your teacher will want you to show your work (or thought process). The calculator is merely a tool to see if you have the right answer or not.
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