This section isn't specifically about Iñupiaq vocabulary or Kaktovik numerals, but may be helpful in understanding how the differences between the Iñupiaq counting system and the English counting systems. The base of a number is represented by the number of symbols used in counting. In English, we start at zero (0), count through nine (9) and enter a new digit at ten (10). We represent the numbers from zero to nine with a different symbol, as follows:
| Symbol | Word |
|---|---|
| 0 | Zero |
| 1 | One |
| 2 | Two |
| 3 | Three |
| 4 | Four |
| 5 | Five |
| 6 | Six |
| 7 | Seven |
| 8 | Eight |
| 9 | Nine |
| 10 | Ten |
We express ten as a "one," followed by a "zero." Then, we begin counting again, starting with eleven (11) and continuing the same way until we get past nineteen (19) and replace the one with a two to get twenty (20). This is known as the decimal system, which fits since "dec-" means "ten."
This is just one of many different number systems, however. One of the most common bases other than this base 10 system is the language of computers- binary. In binary, we only represent numbers in terms of ones and zeroes. This means that when we go from one to two, we have run out of symbols and write two the same way we would write ten (10). Three would be written the same way we write eleven (11), and then we run out of symbols again. Four is written as one hundred (100), followed by five (as 101), six (as 110) and seven (as 111). Once all of the digits are filled with ones, we move to the next place value and write 8 the same way we would normally write a thousand (1000)
| Word | Base 10 (Decimal) | Base 2 (Binary) |
|---|---|---|
| Zero | 0 | 0 |
| One | 1 | 1 |
| Two | 2 | 10 |
| Three | 3 | 11 |
| Four | 4 | 100 |
| Five | 5 | 101 |
| Six | 6 | 110 |
| Seven | 7 | 111 |
| Eight | 8 | 1000 |
This all works fine, since we have plenty of symbols to spare if we want to represent base 2. However, what about when we need more than ten symbols?
Another common number system in programming is the hexadecimal system, which is base 16. In this system, we represent zero through nine in the exact same way we would in the decimal system. However, instead of moving into a new place value when we hit ten, we represent it with "A" instead. Twelve becomes "B," all the way through fifteen represented as "F." We don't move to the next place value until we hit sixteen, which is represented as "10"
| Word | Base 10 (Decimal) | Base 2 (Binary) | Base 16 (Hexadecimal) |
|---|---|---|---|
| Zero | 0 | 0 | 0 |
| One | 1 | 1 | 1 |
| Two | 2 | 10 | 2 |
| Three | 3 | 11 | 3 |
| Four | 4 | 100 | 4 |
| Five | 5 | 101 | 5 |
| Six | 6 | 110 | 6 |
| Seven | 7 | 111 | 7 |
| Eight | 8 | 1000 | 8 |
| Nine | 9 | 1001 | 9 |
| Ten | 10 | 1010 | A |
| Eleven | 11 | 1011 | B |
| Twelve | 12 | 1100 | C |
| Thirteen | 13 | 1101 | D |
| Fourteen | 14 | 1110 | E |
| Fifteen | 15 | 1111 | F |
| Sixteen | 16 | 10000 | 10 |
When we compare the different bases, we can see just how different the numbers can look in the different bases. The difference in what the words and symbols represent will make it difficult to be able to communicate numbers in Iñupiaq, since we need to translate the language and the numbers themselves. This is the issue that led to the development of the Kaktovik numeral system.