If you aren't using a calculator....
For base 16 and base 8, in general anything that's a power of 2, you can convert digits from binary -> whatever easily.
Say you have the number 10001110101100011. Lot of numbers. But it's easy to convert to Hex or Octal. You take the power of 2 you're converting to -- the n in 2^n, for octal it's 2^4, hex it's 2^5 -- subtract 1 and convert that many digits at a time. Confused? A demonstration will help.
Okay, we had the number 10001110101100011. Let's convert to octal first. Octal = base 8 = base 2^4, so we convert 3 digits at a time. Separate the number out in groups of 3, starting from the right.
10|001|110|101|100|011
Like so. Now take each one of those groups of 3 and convert them to the octal equivalents.
10 = 2^1 = 2
001 = 2^0 = 1
110 = 2^1 + 2^2 = 2 + 4 = 6
101 = 2^0 + 2^2 = 1 + 4 = 5
100 = 2^2 = 4
011 = 2^0 + 2^1 = 1 + 2 = 3
So you get 216543 in Octal.
Now let's try hex. Hex = base 16 = base 2^5, so convert 4 digits at a time
1|0001|1101|0110|0011
1 = 2^0 = 1
0001 = 2^0 = 1
1101 = 2^0 + 2^2 + 2^3 = 1 + 4 + 8 = 13 = D
0110 = 2^1 + 2^2 = 2 + 4 = 6
0011 = 2^0 + 2^1 = 1 + 2 = 3
So you have 11D63 in Hex
Unfortunately there's no quick way to convert to decimal, since base 10 isn't a power of 2. From a mathematical standpoint it's almost the worst possible number system to use, short of some prime number-based system. (base 7, base 5, etc.) The only way you can really convert by hand is to add up the powers of 2 in the number:
10001110101100011
= 2^0 + 2^1 + 2^5 + 2^6 + 2^8 + 2^10 + 2^11 + 2^12 + 2^16
= 1 + 2 + 32 + 64 + 256 + 1024 + 2048 + 4096 + 65536 = 73059
Really sucks, but that's the only way to do it.
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