CSCI 112 - Intro To Computer Systems
Binary Place Values
Number System Bases
Base 10:
Decimal, this is the number system you are most familiar with, where every new digit space represents a power of 10, e.g. 321 = (3 * 10^2) + (2 * 10^2) + (1 * 10^0)
Base 2:
Binary, just like Base 10, each digit space represents a power of 2, starting at power 0, e.g.
0101 = (0 * 2^3) + (1 * 2^2) + (0 * 2^1) + (1 * 2^0)
= 0 + 4 + 0 + 1
= 5
Base 8
Octal, this base isn't as wide used, but it can be easily translated to and from binary, as 8 is a power of 2.
36(base 8) = (3 * 8^1) + (6 * 8^0)
= 24 + 6
= 30
Note*: Since 8 is 2 to the power 3, we can use a simple conversion strategy of taking every 3 digits in a binary number and turning it into a number 0-7 to represent the equivalent value in Octal. e.g.
011001 -> (011) (001) -> (3) (1) -> 31(base 8)
Base 16
Base 16:
Hexadecimal(Hex), a very common base system, this can be used to compress an 8 digit binary number into just 2 digits. To do so, we use the same 'trick' we used for base 8, except we use 4 binary digits as 16 is 2^4. Hex is a bit unique, as it uses A-F to represent 10-15 where
[A:10, B:11, C:12, D:13, E:14, F:15]
Here is an example conversion:
00111101 -> (0011) (1101) -> (3) (D[13]) -> 3D
