4-Bit Binary
The computer language of 0s and 1s.
What is Binary?
- Computers store and use data as a series of 0s and 1s.
- This system is called binary because it only has two options: on or off.
- It’s like a set of light switches: 0 means off, and 1 means on.
Binary and Denary
- Denary is the number system we use every day (0–9).
- Binary is how computers count, using only 0 and 1.
How to Convert Between Binary and Denary
Binary to Denary (Computer to Human Numbers)
Each binary digit (0 or 1) represents a value. Think of it as switches for different amounts:
| Switch Value | 8 | 4 | 2 | 1 |
|---|---|---|---|---|
| Binary Number | 1 | 1 | 0 | 1 |
If the switch is 1, add that value:
- In this example: 8 + 4 + 0 + 1 = 11
- So, 1101 in binary = 13 in denary
Denary to Binary (Human Numbers to Computer)
Start with a number and turn on switches (1) for the biggest values that fit.
Example: Convert 9 to binary:
- 9 can use the 8 switch → turn it on (1)
- 1 is left over → turn on the 1 switch
- Fill the rest with 0
| Switch Value | 8 | 4 | 2 | 1 |
|---|---|---|---|---|
| Binary Number | 1 | 0 | 0 | 1 |
So, 9 = 1001 in binary
Key Points
- Computers use binary (0s and 1s) to store information
- Binary to Denary: Add the values for switches turned on
- Denary to Binary: Turn on switches (1) starting with the biggest values that fit