Arithmetic
Counting
In mathematical problems, there is a difference between the way you count numbers and values. In simple base 10 math, the methods appear to be the same; However, if you intend to use an alternative base for your mathematical problems, you can immediately see the difference.
A numerical representation for a value, is divided into exponents according to it's base. For example, in base 10 math, the digits representing values are read from right to left as ones, tens, hundreds, thousands, etc. - which are all multiples of 10.
In base two math, they read from right to left as ones, twos, fours, eights. Similarly, base three math reads ones, threes, nines, twenty-sevens, etc.
The following table illustrates the four basic digits that represent values for each base up to ten.
Base One |
D.N.E. |
D.N.E. |
D.N.E. |
D.N.E. |
|
Base Two |
1 = 1 |
10 = 2 |
100 = 4 |
1000 = 8 |
|
Base Three |
1 = 1 |
10 = 3 |
100 = 9 |
1000 = 27 |
|
Base Four |
1 = 1 |
10 = 4 |
100 = 16 |
1000 = 64 |
|
Base Five |
1 = 1 |
10 = 5 |
100 = 25 |
1000 = 125 |
|
Base Six |
1 = 1 |
10 = 6 |
100 = 36 |
1000 = 216 |
|
Base Seven |
1 = 1 |
10 = 7 |
100 = 49 |
1000 = 343 |
|
Base Eight |
1 = 1 |
10 = 8 |
100 = 64 |
1000 = 512 |
|
Base Nine |
1 = 1 |
10 = 9 |
100 = 81 |
1000 = 729 |
|
Base Ten |
1 = 1 |
10 = 10 |
100 = 100 |
1000 = 1000 |
|
Addition
Addition, like all mathematical operations, is not dependent on the base you are using. To perform addition, you simply count inside of a placeholder until it carries over into the next place.
For example:
Base 2:
101 + 1 = 110 (5 + 1 = 6)
Because base 2 math only allows 1's and zeros, you must carry over any remaining digits.
Subtraction
Multiplication
Division
Exponents
Roots
Irrational/Fractional Numbers