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WEEK 5
TOPIC: Counting in Base Two
CONTENTS:
- Counting in group of twos.
- Conversion from base 10 numerals to binary numbers.
- Conversion from binary to decimal
NUMBER BASES
In Mathematics, a base or radix is the number of different digits or combination of digits and letters that a system of counting uses to represent numbers. For example, the most common base used today is the decimal system. Because “dec” means 10, it uses the 10 digits from 0 to 9. Most people think that we most often use base 10 because we have 10 fingers.
A base can be any whole number bigger than 0 (if it was 0, then there would be no digits). The base of a number may be written next to the number: for instance, 23 8 {\displaystyle 23_{8}\ } 238 means 23 in base 8 (which is equal to 19 in base 10).
| NUMBER OF BASE | DIGITS USED | NAMES |
| 2 | 0, 1 | Binary |
| 3 | 0, 1, 2 | Ternary |
| 4 | 0, 1, 2, 3 | Quaternary |
| 5 | 0, 1, 2, 3, 4 | Quinary |
| 6 | 0, 1, 2, 3, 4, 5 | Senary |
| 7 | 0, 1, 2, 3, 4, 5, 6 | Septenary |
| 8 | 0, 1, 2, 3, 4, 5, 6, 7 | Octal |
| 9 | 0, 1, 2, 3, 4, 5, 6, 7, 8 | Nonary |
| 10 | 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 | Decimal/ denary |
| 11 | 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 | Undecimal |
| 12 | 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B | Duodecimal |
| 16 | 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F | Hexadecimal |
| 20 | 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, G, H, I, J | Vigesimal |
The popularity of the base 2, 8 and 16 is because of its use in modern technology.
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