Syllabus Detail
- Number systems; binary, decimal, hexadecimal 11ATAR
Background
- A number system is a writing system for expressing numbers
- These mathematical notations can be presented using digits or other symbols
- Number systems are an integral part of a computer system as they provide the backbone of processing and computing
- Computer's utilize three main number systems; binary, decimal and hexadecimal
The Binary number system
- The binary number system is a base-2 number system that consists of only two digits: 0 and 1
- These digits represent the state of which a computer switch can fall under, with 0 commonly referring to off and 1 referring to on
- The short name for a binary digit is a bit (the smallest amount of information available in a computer system)
- Binary works by using 0's and 1's to represent the value of larger numbers
- Each value of a digit in binary is double that of the number to the right of it
- If a "1" is placed in a values column, we add that value to the total count to get our number
- Example:
-
| Value |
8 |
4 |
2 |
1 |
| Binary |
1 |
1 |
0 |
1 |
| Number |
13 |
5 |
1 |
1 |
(Hint: Read from right to left. The binary number 1101 is equal to 13.)
The Decimal number system
- The decimal number system is a base-10 number system and is one we use on a day-to-day basis
- A decimal number system uses the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 to represent numbers
- These numbers use a decimal seperator (full-stop or period) to indicate a fraction
- We use a + symbol to represent a positive number, and a - symbol to represent a negative number
- The properties of the decimal number system make it hard for a computer to be fully accurate when rounding with numbers
- This is because computers work with a base-2 number system (binary)
- These numbers get less accurate the bigger or smaller they get (often both extremities)
- These inaccuracies are often minute and still offer far more reliability than a person!
The Hexadecimal number system
- The hexadecimal (hex) number system is a base-16 number system
- It utilizes the decimal system's 10 digits (0, 1, ..., 9) as well as an additional 6 characters (A, B, C, D, E, F)
- Hexadecimal values are widely used by programmers and developers as they allow for writing large values easily
- This notation is often used to reference colour options
- E.g. the HEX value #FF0000 is the equivalent colour of red
- Hex values can be written in capitals or lowercase
Further Research
- Read more about Binary Numbers at CSUnplugged.org here
- 3 Ways to Understand Hexadecimal at WikiHow here
- Read more about the numeral systems on RapidTables here
- Convert between binary, decimal and hexadecimal with an online converter
Worksheet and Practice (yet to be added)
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