Hexadecimal	Decimal	Octal	Base 4	binary
0	0	0	0	0
1	1	1	1	1
2	2	2	2	10
3	3	3	3	11
4	4	4	10	100
5	5	5	11	101
6	6	6	12	110
7	7	7	13	111
8	8	10	20	1000
9	9	11	21	1001
A	10	12	22	1010
B	11	13	23	1011
C	12	14	30	1100
D	13	15	31	1101
E	14	16	32	1110
F	15	17	33	1111

You can see that 1 hexadecimal digit represents 4 binary digits exactly, 1 octal digit represents 3 binary digits exactly and 1 base 4 digit represents 2 binary digits exactly. However a decimal digit is not an exact representation of any number of binary digits.

This is useful because if I want to convert a binary number to hexadecimal I can do it in groups of 4 digits using the conversion table above and vis versa

i.e.
1110001010110111
splits into
1110 = E
0010 = 2
1011 = B
0111 = 7

so Binary(1110001010110111) = Hexadecimal(E2B7)

Any project needs to demonstrate this relationship as it is this that gives hexadecimal it usefulness and has caused it to become so prevalent in the computer world.

The relationship between hexadecimal(base 16), octal(base 8) base 4 and binary(base 2) is that the bases are all powers of 2. Note that base 16 is also a power of 4 (squared)and in fact from above 1 hexadecimal digit is also represents the exactly the same values as 2 base 4 digits.

A similar relationship exists between bases 3 and 9.