Numeral System

A way of noting down numbers (for mathematics).

Place values

3 4 3           
^ ^ ^           
| | |           
| | ones (units)
| |             
| tens          
|               
hundreds        

0, 1, 2, 3, 4, 5, 6, 7, 8, 9... 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22 [...] 98, 99... 100, 101, 102...

In our standard system is decimal (base-10), consiting of 10 numbers (0-9). 0 represents nothing and 1 the first something. We count from 1 to 9, and when we reach the highest number in our system - 9 - the next number becomes double digit. We start with zero again with a one added to the left - 10. Then we count the right number up until 19, then the left number goes up again - 20. It can go up to 99 like this, then the number is again replaced with zeroes with a one added to the start - 100. Digits can be added like this as much as necessary. Our system is decimal or base-10, other numeral systems use range of numbers is different from 0-9.


Non-decimal numeral systems

Hexadecimal (base-16): 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F... 10, 11, 12...

Binary, (base-2): 0, 1... 10, 11... 100, 101, 110, 111... 1000, 1001, 1010, 1011, 1100, 1101...

Octal (base-8): 0, 1, 2, 3, 4, 5, 6, 7... 10, 11, 12, 13, 14, 15, 16, 17, 20, 21 [...] 75, 76, 77, 100


Unique place value numeral systems

Mayan, vigesimal (base-20):

0 - 0, * - 1, - - 5

0, *, **, ***, ****, -, *-, **-, ***-, ****-, --, *--, **--, ***--, ****--, ---, *---, **---, ***---, ****---... -*

Sumerian, sexagesimal (base-60):

i - 1, X - 10, I - 60

i, ii, iii, iiii, iiiii, iiiiii, iiiiiii, iiiiiiii, iiiiiiiii, X, Xi, Xii, Xiii, Xiiii, Xiiiii, Xiiiiii, Xiiiiiii, Xiiiiiiii, Xiiiiiiiii, XX, XXi [...] XXXXXiiiiiiii, XXXXXiiiiiiiii, I, Ii, Iii...

Roman:

I - 1, V - 5, X - 10, L - 50, C - 100, D - 500, M - 1000

I, II, III, IV, V, VI, VII, VIII, IX, X, XI, XII, XIII, XIV, XV, XVII, XVII, XVIII, XIX, XX, XXII, XXIII...


Unary

A unary numeral system is the idea of noting numbers using a single symbol. The "traditional" way of doing unary is to write down the number by writing "that amount" of symbols.

0, 00, 000, 0000, 00000, 000000, 0000000, 00000000, 000000000, 0000000000, 00000000000...