Digital Electronics

Digital electronics is a field that focuses on digital signals, where information is represented using binary code—only 0s and 1s instead of continuous analog signals . It involves the design and operation of devices that generate, process, or respond to these signals. From logic gates and resistors to amplifiers and integrated circuits, digital electronics forms the backbone of today’s electronic devices.

Digital electronics is a vital skill in the tech world. Whether you’re a student, hobbyist, or aspiring engineer, understanding how digital systems work opens up countless career opportunities in VLSI design, embedded systems, IoT and more.

 

What are Number Systems in Digital Electronics and Why Are They Important?

Digital systems like computers, microcontrollers, FPGAs and Embedded Systems fundamentally operate using binary (base-2) numbers. The most basic language of electronics where every bit represents either a 0 (OFF) or 1 (ON). But why do we need other number systems?

  • Humans naturally calculate in decimal (base-10)
  • Programmers use hexadecimal (base-16) for compact code representation
  • System designers occasionally use octal (base-8) for specific applications

This comprehensive guide explains all key number systems with conversion methods and real-world applications – essential knowledge for anyone working with digital technology.

Complete Comparison of Digital Number Systems

System Base Digits Example Primary Usage
Binary 2 0,1 10110 CPU operations, digital circuits
Decimal 10 0-9 18 Everyday calculations
Octal 8 0-7 16 Legacy Unix systems
Hex 16 0-9,A-F B4 Memory addressing, programming

 

What is Binary Number System (Base-2)?

Binary number system is a base-2 number system that uses only two independent digits: 0 and 1. This system is fundamental to digital electronics and computing because electronic circuits are designed to recognize two distinct voltage levels, which correspond directly to the binary digits 0 (representing OFF or LOW) and 1 (representing ON or HIGH).

What are the best methods to convert decimal numbers to binary?

Method 1: Division by 2 (Recommended)

Step-by-Step Process

    1. Divide the decimal number by 2
    2. Record the remainder (0 or 1)
    3. Repeat with the quotient until it becomes 0
    4. The binary number is the remainders read from bottom to top

Example: Convert 10 to Binary

Division Quotient Remainder
10 ÷ 2 5 0
5 ÷ 2 2 1
2 ÷ 2 1 0
1 ÷ 2 0 1

Result: 10 in decimal = 1010 in binary

Method 2: Subtraction Using Powers of 2

Step-by-Step Process

    1. List powers of 2 (1, 2, 4, 8, 16, 32…)
    2. Find the highest power ≤ your number
    3. For each power: If you can subtract it from the remaining value: Place 1 else 0 in that position
    4. Repeat with remainder until you reach 0

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Example: Convert 10 to Binary

    1. Find the highest power of 2 ≤ 10 → 8 (2³)
        • 10 – 8 = 2 → 1 in the 2³ place
    2. Next power → 4 (2²)
        • 2 < 4 → 0 in the 2² place
    3. Next power → 2 (2¹)
        • 2 – 2 = 0 → 1 in the 2¹ place
    4. Final power → 1 (2⁰)
        • 0 < 1 → 0 in the 2⁰ place

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Binary Representation: 1010

Verification

    • 1×2³ + 0×2² + 1×2¹ + 0×2⁰ = 8 + 0 + 2 + 0 = 10

 

What is the Octal Number System?

The Octal Number System is a base-8 number system widely used in digital electronics and computing. It simplifies binary representations, making it easier for programmers and engineers to work with large binary numbers. The Octal Number System uses 8 digits (0-7) to represent numbers. Each position in an octal number represents a power of 8.

What are the best methods to convert decimal numbers to octal?

Step-by-Step Process

    1. Group binary digits in sets of three, starting from the right.
    2. Replace each triplet with the corresponding octal digit.

Example: Convert 54 to Octal

    1. Group into 3-bit sets:
        • 101 100

    2. Convert each group:
        • 101 → 5

        • 100 → 4

    3. Final octal number: 55₈

What is the Decimal Number System?

The decimal number system, also known as base-10, is the most widely used number system and is fundamental to mathematics and digital Electronics. The Decimal Number System uses 10 digits (0-9)  to represent numbers. Each position in an octal number represents a power of 10.

What are the best methods to convert binary numbers to decimal?

Method 1: Division by 2 (Remainder Method)

Steps:

    1. Divide the decimal number by 2
    2. Record the remainder (0 or 1)
    3. Repeat with the quotient until it reaches 0
    4. Reverse the remainders to get the binary result

Example: Convert 25 to Binary

Division Quotient Remainder
25 ÷ 2 12 1 (LSB)
12 ÷ 2 6 0
6 ÷ 2 3 0
3 ÷ 2 1 1
1 ÷ 2 0 1 (MSB)

Result: 11001₂ (Read remainders from bottom to top)

Method 2: Subtraction Using Powers of 2

Steps:

    1. List powers of 2 (1, 2, 4, 8, 16, 32, 64, 128…)
    2. Find the highest power ≤ decimal number
    3. Subtract & mark 1 for used powers, 0 for unused
    4. Combine 1s and 0s from left to right

Example: Convert 43 to Binary

Power of 2 64 32 16 8 4 2 1
Used? 0 1 1 0 1 0 1

Calculation:

    • 32 (1) → 43 – 32 = 11

    • 16 (0, too large)

    • 8 (1) → 11 – 8 = 3

    • 4 (0, too large)

    • 2 (1) → 3 – 2 = 1

    • 1 (1) → 1 – 1 = 0

Result: 101011₂

What is the HexaDecimal Number System?

The Hexadecimal number system, also known as base-16, is the most widely used number system and is fundamental to mathematics and digital Electronics. The HexaDecimal Number System uses 16 digits (0-F)  to represent numbers. Each position in an octal number represents a power of 16.

What are the best methods to convert decimal numbers to hexadecimal?

Method 1: Division by 16 (Remainder Method)

Steps:

    1. Divide the decimal number by 16
    2. Record the remainder (0-9 or A-F)
    3. Repeat with the quotient until it reaches 0
    4. Reverse the remainders to get the hex result

Example: Convert 255 to Hexadecimal

Division Quotient Remainder (Hex)
255 ÷ 16 15 15 (F)
15 ÷ 16 0 15 (F)

Result: FF₁₆ (Read remainders from bottom to top)

Method 2: Using Powers of 16 (Subtraction Method)

Steps:

    1. List powers of 16 (1, 16, 256, 4096…)
    2. Find the highest power ≤ decimal number
    3. Divide & record the hex digit (0-F)
    4. Repeat with the remainder

Example: Convert 300 to Hexadecimal

    1. Highest power ≤ 300: 256 (16²)
        • 300 ÷ 256 = 1 → Remainder: 44

    2. Next power (16):
        • 44 ÷ 16 = 2 → Remainder: 12

    3. Last power (1):
        • 12 ÷ 1 = 12 (C)

    4. Combine digits: 
        • 1 2 C → 12C₁₆

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