LESSON 2: CONVERSION BETWEEN DECIMAL AND BINARY SYSTEMS

Lesson Outcomes

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

  • Understand binary numbers and how they work
  • Convert between decimal and binary systems
  • Perform binary arithmetic operations
  • Apply the BODMAS rule in calculations

Lesson Overview

This lesson introduces learners to the binary number system, which is fundamental to all digital systems and computing technologies. Unlike the decimal system (base 10), binary uses only two digits: 0 and 1.

Binary is used in computers because it aligns with the electrical states of hardware — on (1) and off (0). Understanding binary is essential for working with programming, automation, and RPA tools.

What is Binary?

Binary is a base-2 number system that uses only two digits: 0 and 1.

It is used at the core of all digital computers to:

  • Encode information
  • Perform arithmetic operations
  • Execute logical processes

Using only two digits allows systems to operate using simple electrical signals (on/off states), which form the foundation of computing systems.

Binary vs Decimal System

  • Decimal system (base 10): Uses digits 0–9

  • Binary system (base 2): Uses only 0 and 1

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

Binary Number Example

Binary numbers are calculated using powers of 2:

Example:
10011 (binary)

= (1 × 2⁴) + (0 × 2³) + (0 × 2²) + (1 × 2¹) + (1 × 2⁰)
= 16 + 0 + 0 + 2 + 1
= 19 (decimal)

Understanding Binary Place Values

Each position in a binary number represents increasing powers of 2:

Binary Position Power of 2 Value
1 2³ 8
1 2² 4
0 2¹ 0
0 2⁰ 0

Example:
1100 (binary) = 12 (decimal)

Binary Arithmetic

Binary arithmetic includes:

  • Addition
  • Subtraction
  • Multiplication
  • Division

These operations are simpler than decimal arithmetic because only two digits are used.

Binary Addition Rules

There are four basic rules:

  1. 0 + 0 = 0

  2. 0 + 1 = 1

  3. 1 + 0 = 1

  4. 1 + 1 = 10 (carry 1 to the next column)

Binary addition is essential for all digital computations.

Binary Subtraction

Binary subtraction involves borrowing, similar to decimal subtraction.

Binary Multiplication

Binary multiplication is similar to decimal multiplication but simpler because only 0 and 1 are used.

Binary Division

Binary division follows the same principles as long division in decimal systems.

Binary Arithmetic Importance

Binary arithmetic is essential in digital systems because:

  • It enables computers to process data
  • It simplifies calculations at hardware level
  • It supports logical and computational operations

BODMAS Rule

The BODMAS rule helps determine the correct order of operations in calculations.

BODMAS stands for:

  • B – Brackets

  • O – Order (powers, roots)

  • D – Division

  • M – Multiplication

  • A – Addition

  • S – Subtraction

How BODMAS Works

When solving an expression:

  1. Solve brackets first
  2. Then powers or roots
  3. Then division and multiplication (left to right)
  4. Then addition and subtraction (left to right)

Example:
5 + 3 × 2 = 11 (not 16, because multiplication comes first)

Lesson Summary

In this lesson, learners explored:

  • The binary number system and its importance
  • Differences between binary and decimal systems
  • How to convert binary to decimal
  • Basic binary arithmetic operations
  • The BODMAS rule for correct calculation order

These concepts are fundamental for programming, automation, and working with digital systems in RPA.

 

PreviousNext