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Reading Journal
Computers use base systems to help shorten the information they use via a method known as positional notation. Positional notation allows for a vastly smaller amount of characters to be used to represent much larger numbers. The way positional notation works with base systems is that the value furthest to the right is multiplied by 1. Then each position to the left has its multiplication factor changed by whatever value the base system is. For example, in a base 2 system such as binary the right most value is multiplied by 1, then one position to the left is multiplied by 2, then the next position is multiplied by 4 and then 8 and then 16 and so on. For any base system that uses more than ten symbols(0-9), the alphabet is then used and is known as alphanumerics.. An example would be how hexadecimal, which is base 16, uses a-f to represent 10-15. Other base systems use the whole alphabet and even create more characters by being case sensitive. Below is an example of how a base two system using positional notation works:
| 256 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
| 0 | 0 | 1 | 0 | 0 | 1 | 1 | 0 |
| 0+ | 0+ | 32+ | 0+ | 0+ | 4+ | 2+ | 0 |
Is equal to 38.
The top row shows positional notation, each number is twice as large as the one to the right. The row shows which positions have values. The bottom row shows how each position is factored into the equation. The positional notation value is multiplied by the imputed values and then the product of that equation is added to the rest to determine the final value the system is representing.
Sources:
Athapathu, Rukshani. “Hexadecimal Notation.” Medium, Coder’s Corner, 26 May 2018, medium.com/coderscorner/hexadecimal-notation-c696eb32328a.
Athapathu, Rukshani. “Number Systems - Decimal, Binary, Octal and Hexadecimal.” Medium, Coder’s Corner, 25 Aug. 2018, medium.com/coderscorner/number-systems-decimal-binary-octal-and-hexadecimal-5e567e55ab28.
Athapathu, Rukshani. “Signed and Unsigned Numbers.” Medium, Coder’s Corner, 13 May 2018, medium.com/coderscorner/signed-and-unsigned-numbers-c8cdc54bff87.
“Binary Numbers and Base Systems as Fast as Possible.” YouTube, YouTube, 15 June 2014, www.youtube.com/watch?v=LpuPe81bc2w.