Heres some ways i used which where fast for the exam:
Decimal to Binary
Eg number 78:
1) Draw out the powers of 2 from 2^0 to [an appropriate max] from RIGHT TO LEFT along a piece of paper. (for those that dont think that way.. start at 1 and double it until u get along to a large enough number)
128--64--32--16--8--4--2--1--
2) now find the max number which fits in 78 from the above line and subtract it from 78.
78 - 64 = 14 : so we know the number 78 contains 1 lot of 64 so we place a 1 at 64 like so....
........1
128--64--32--16--8--4--2--1--
Now the next highest is 8 because 14 - 8 = 6 and 16 does not fit into 14. so place a one at 8.
........1..............1
128--64--32--16--8--4--2--1--
Now we are only left with 6 so 6 -4 = 2...... and the next step is 2-2 = 0 so we place a '1' at 4 and the next step is to place '1' at 2. Then finally fill in the zeros to the right of the most significant bit.
........1....0....0...1..1..1..0
------64--32--16--8--4--2--1----------------- as shown the answer is 1001110
Binary to Hex
lets use the same number as before. 1001110
1) we first write down the number and split it into groups of 4 bits (a nibble if i remember correctly) from the right to the left
[0100][1110]
Now count up the value of each nibble starting from 2^0 at each bracket ]
i.e.
[0100] and [1110]
-8421-------8421-
= =
4 14
Now 4 in HEX is 4. and 14 in HEX is E why?? [0123456789ABCDEF]
so the anser is 0x4E (0x is just a term to used to show the number is HEX..not needed)
Not sure if you need octal or that. But those are the two most common. And u can use those 2 to convert from decimal to hex if needed, and hex to decimal is the exact opposite of what i did above. Hope this is a little less confusing than other sources.
P.S. [Edit] sorry about all the dots and dashes... this forum removed my spaces
