Digital Electronics Study Notes

Introduction to Digital Electronics; Signals: Analog vs Digital; Number Systems

Introduction to Digital Electronics

Digital electronics is the branch of electronics that deals with discrete (digital) signals — voltages that represent only two logical states: 0 (LOW) and 1 (HIGH). Unlike analog electronics where signals vary continuously, digital systems use binary logic to represent, process and transmit information.

Why Digital?

Building Blocks

Input → [Logic Gates] → [Combinational/Sequential Circuits] → Output
 ↓
 Flip-Flops, Registers, Counters

Every digital system — from a calculator to a CPU — is built from these fundamental blocks.

Signals: Analog vs Digital

2.1 Analog Signal

An analog signal is a continuous time-varying quantity. One physical variable represents another.

• Waveform: Sine wave
• Values: Infinite between min and max
• Examples:

Temperature sensors, FM radio, photocells, resistive touch screens

• Bandwidth: Low

- Noise: More susceptible

• Accuracy: Less accurate measurement

2.2 Digital Signal

A digital signal represents data as a sequence of discrete values at specific time instants — typically 0 and 1.

• Waveform: Square wave
• Values: Only 0 and 1
• Examples: Computers, CDs, DVDs,

microprocessors

• Bandwidth: High
• Noise: Less susceptible
• Accuracy: Highly

accurate

2.3 Comparison Table

Key insight: Modern systems often convert analog → digital (ADC) for processing, then digital → analog (DAC) for output.

Number Systems

A number system defines how numbers are written using digits and place values.

3.1 Non-Positional Number System

Each symbol has the same value regardless of position.

• Example: Roman numerals — I=1, II=2, III=3, IV=4
• Disadvantage: Arithmetic is very

difficult

• Historical use only

3.2 Positional Number System

Each digit's value depends on its position (place value).

General form for base *b*:

\[ N = d_n \times b^n + d_{n-1} \times b^{n-1} + \cdots + d_1 \times b^1 + d_0 \times b^0 \]

Where:

• b = base (radix)
• dᵢ = digit at position i (0 ≤ dᵢ < b)

3.3 Major Number Systems in Digital Electronics

3.4 Decimal Example (Base 10)

Number: 4567

\[ 4567 = 4 \times 10^3 + 5 \times 10^2 + 6 \times 10^1 + 7 \times 10^0 = 4000 + 500 + 60 + 7 \]

3.5 Binary (Base 2)

• Only digits 0 and 1
• Each position = power of 2
• n bits → 2ⁿ distinct values

Example: (1011)₂

\[ = 1 \times 2^3 + 0 \times 2^2 + 1 \times 2^1 + 1 \times 2^0 = 8 + 0 + 2 + 1 = (11)_{10} \]

3.6 Octal (Base 8)

• Digits 0–7
• 1 octal digit = 3 binary digits
• Used for compact representation of

binary strings

3.7 Hexadecimal (Base 16)

• Digits 0–9, A=10, B=11, C=12, D=13, E=14, F=15
• 1 hex digit = 4 binary digits

- Standard in programming and memory dumps

3.8 Conversion Table (0–15)