Artificial Intelligence Software Developer

Learning Outcomes

By the end of this lesson, learners will be able to:

Understand the binary number system
Convert decimal numbers to binary
Convert binary numbers to decimal
Perform binary arithmetic

1. Introduction to Binary Numbers

The binary number system is a base-2 numbering system used by computers.

Unlike the decimal system (base 10), binary uses only two digits:

0
1

Computers use binary because electronic circuits have two states:

State	Binary Value
Off	0
On	1

Every piece of data processed by a computer is represented using binary numbers.

2. Binary Place Values

Each digit in a binary number represents a power of 2.

Power of 2	Value
2^0	1
2^1	2
2^2	4
2^3	8
2^4	16
2^5	32

Example binary number:

1011

Represents:

(1 × 2^3) + (0 × 2^2) + (1 × 2^1) + (1 × 2^0)

3. Converting Binary to Decimal

Example:

10101

Step-by-step conversion:

(1 × 2^4) + (0 × 2^3) + (1 × 2^2) + (0 × 2^1) + (1 × 2^0)

16 + 0 + 4 + 0 + 1

So:

10101 (binary) = 21 (decimal)

4. Converting Decimal to Binary

Example: Convert 19 to binary.

Divide repeatedly by 2.

Division	Remainder
19 ÷ 2 = 9	1
9 ÷ 2 = 4	1
4 ÷ 2 = 2	0
2 ÷ 2 = 1	0
1 ÷ 2 = 0	1

Read remainders from bottom to top.

10011

So:

19 (decimal) = 10011 (binary)

5. Binary Addition

Binary addition follows these rules:

Addition	Result
0 + 0	0
0 + 1	1
1 + 0	1
1 + 1	10

Example:

1011
+0101

Step-by-step result:

10000

6. Binary Arithmetic in Computing

Binary arithmetic is used in:

computer processors
digital circuits
memory storage
programming
encryption systems

Every operation performed by a computer is based on binary calculations.

7. Example in Programming

Binary logic is used in programming languages.

Example condition:

if (binaryValue == 1)

Binary operations are also used in:

bitwise operations
network protocols
file encoding

Real-World Example

A pixel in an image is stored as binary data.

Example RGB pixel values:

Color	Binary
Red	11111111
Green	00000000
Blue	00000000

This represents a pure red pixel.

Lesson Summary

In this lesson we learned:

Binary numbers use base 2
Computers process information using 0 and 1
Binary numbers can be converted to decimal
Decimal numbers can be converted to binary
Binary arithmetic follows simple rules