Lesson Objective
- Understand the use of Binary.
- Be able to convert base 2 numbers to base 10.
- Be able to convert base 10 numbers to base 2.
mrahmedcomputing
KS3, GCSE, A-Level Computing Resources
Lesson 1. Binary
Lesson Notes
Number Systems
A numeral system is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner.
Denary (Decimal) Number System
Decimal (or Denary) has 10 digits (0-9), and can be referred to as "base 10". Numbers are organised in multiples of ten's.
Here are examples of Base 10 numbers:
| 1000s | 100s | 10s | 1s |
|---|---|---|---|
| 0 | 0 | 0 | 6 |
| 0 | 1 | 5 | 8 |
| 3 | 4 | 2 | 3 |
Binary Number System
Binary has two digits 0 and 1, and is referred to as base 2.
- Binary is the language computers understand.
- Computers only work with values of 1 and 0.
- The reason for this is computers work on circuit boards where there is either high voltage (1) or low voltage (0).
Binary uses only 2 digits, 1 and 0 and each place value goes up in multiples of 2 instead of 10, like the decimal system.
Here are examples of Base 2 numbers:
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
| 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 |
| 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 |
| 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 |
| 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 |
| 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 |
| 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 |
| 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 |
The row highlighted blue shows the Base 10 number 57.
(128*0)+(64*0)+(32*1)+(16*1)+(8*1)+(4*0)+(2*0)+(1*1) = 57.
This shows that 32 + 16 + 8 + 1 = 57.
We don't include the 128, 64, 4 or 2 as they have 0's in their place values.