BINARY NUMBERS OVERVIEW
Base 10 Number System
Each digit’s position in a number represents an integer value ranging from 0 to 9.
Let’s break down the base 10 number 13:
| 10^1 | 10^0 |
|---|---|
| 1 | 3 |
- The leftmost digit represents 10^1, which equals 10;
- The rightmost digit represents 10^0, which equals 1;
When I sum up these values:
> (1x10^1) + (3x10^0)
> (1x10) + (3x1)
> 10 + 3 = 13
Binary Number System
- Binary numbers are represented using only two symbols: 0 (off) and 1 (on);
- Each digit’s position represents a power of 2;
- The rightmost digit represents 2^0, the next one ^1, then 2^2, and so on;
So, let’s break down the binary number 1010:
| 2^3 | 2^2 | 2^1 | 2^0 |
|---|---|---|---|
| 1 | 0 | 1 | 0 |
- The leftmost digit represents 2^3, which equals 8;
- The next digit to the left represents 2^2, which equals 4;
- The next digit to the left represents 2^1, which equals 2;
- The rightmost digit represents 2^0, which equals 1;
When I sum up these values:
> 2^3 + 2^2 + 2^1 + 2^0
> (1x2^3) + (0x2^2) + (1x2^1) + (0x2^0)
> 8 + 0 + 2 + 0 = 10
> 1010 = 10
Byte and Bit Sizes
| Unit | Size |
|---|---|
| Byte | 1 |
| Bits | 8 |
- 1 byte consists of 8 bits.
Binary Positional Notation
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
- Binary numbers are represented using 8 bits;
- Each bit represents a specific value, ranging from 1 to 128;
Binary Counting
- Computers count in binary, starting from 0 to 255;
- The value 255 is represented by setting all bits to 1 in a byte;