### 1. Signals

A signal is a function that conveys information about the behavior or attributes of some phenomenon. In digital electronics, we mainly deal with two types of signals: analog and digital signals.

#### 1.1 Analog Signal

An analog signal is a continuous signal that changes over time. It can have an infinite number of values in a range. For example, the sound produced by human speech, temperature variations, etc.

#### 1.2 Digital Signal

A digital signal is a discrete-time signal which only has two states: HIGH (usually representing a binary 1) and LOW (representing a binary 0). Digital signals are more resilient to noise, and hence, more reliable for transmitting information. They are fundamental to digital electronics and computer processing.

#### 1.3 Discrete Signal

A discrete signal is a physical quantity that is not continuous, i.e., it changes only at specific times and has only a certain set of possible values. This is in contrast to analog signals which are time-variant and continuous.

#### 1.4 Clock Signal and Clock Pulse

A clock signal is a type of signal that oscillates between a high and a low state and is used to coordinate the actions of two or more circuits. A clock pulse is a specific type of digital signal that periodically transitions between two levels, often used as a timing base for synchronous digital circuits.

### 2. Introduction to Digital Systems

A digital system is a system that handles digital signals. It includes devices like computers, calculators, and digital watches that perform calculations and operations in binary form. This form consists of data in the format of zeros and ones, where each of these digits is considered a bit. These systems have digital logic gates to perform logical and arithmetic operations.

### 3. Number System

A number system is a way to represent numbers. In digital electronics, we primarily work with the Binary, Decimal, Octal, and Hexadecimal number systems. Conversion between these number systems is essential in digital electronics.

#### 3.1 All Conversions

It's important to know how to convert between binary, decimal, octal, and hexadecimal number systems. While conversion between decimal and binary/octal/hexadecimal forms involves division and multiplication by 2, 8, and 16 respectively, conversion between binary and octal/hexadecimal is more straightforward as they are all powers of two.

### 4. Binary Arithmetic

Binary arithmetic is similar to decimal arithmetic, the only difference being that only two digits, 0 and 1, are used in binary arithmetic. We have four main operations in binary arithmetic.

#### 4.1 Addition

Binary addition follows these rules:

- 0 + 0 = 0
- 0 + 1 = 1
- 1 + 0 = 1
- 1 + 1 = 0 (with a carry of 1)

#### 4.2 Subtraction

Binary subtraction follows these rules:

- 1 - 0 = 1
- 0 - 0 = 0
- 0 - 1 = 1 (borrow 1)
- 1 - 1 = 0

#### 4.3 Multiplication

Binary multiplication is like logical AND operation. The rules are:

- 0 * 0 = 0
- 0 * 1 = 0
- 1 * 0 = 0
- 1 * 1 = 1

#### 4.4 Division

Binary division is the repeated process of subtraction. The dividend is subtracted from the divisor until the dividend is less than the divisor, at which point the remainder and quotient are noted.

#### 4.5 1's Complement and 2's Complement

The 1's complement of a binary number is the number that results from flipping all bits in the original binary number. The 2's complement is the binary number obtained by adding 1 to the 1's complement of a binary number. The 2's complement is often used to represent negative numbers in binary.

#### 4.6 Subtraction using 2's Complement

The subtraction of binary numbers can be done by the addition of 2's complement. The minuend remains the same, but the subtrahend is replaced by its 2's complement, and then addition is performed. If carry is generated, it is discarded.

### 5. Logic Gates

Logic gates are the basic building blocks of any digital system. They are used to implement boolean logic, which is the backbone of digital electronics. There are seven basic logic gates: AND, OR, XOR (Exclusive OR), NOT, NAND (NOT AND), NOR (NOT OR), and XNOR (Exclusive NOR).

#### 5.1 Conversion, IC number in Proteus, Truth Table

Every logic gate has a corresponding Integrated Circuit (IC) number which can be used to simulate the gate in Proteus software. For example, the IC number for the AND gate is 7408. The truth table represents the relationship between the input and the output of a gate.

### 6. Adders and Subtractors

Adders and subtractors are key components of digital computers. They are used to perform addition and subtraction operations, respectively.

#### 6.1 Half Adder and Half Subtractor

A half adder is a combinational circuit that performs the addition of two bits and outputs a SUM and a CARRY. A half subtractor performs subtraction of two bits and outputs a DIFFERENCE and a BORROW.

#### 6.2 Full Adder and Full Subtractor

A full adder is a combinational circuit that performs the addition of three bits and outputs a SUM and a CARRY. It is used when there is a carry from the previous bit in a multi-bit addition operation. A full subtractor performs subtraction of three bits (minuend, subtrahend, and borrow) and outputs a DIFFERENCE and a BORROW. It is used when there is a borrow from the previous bit in a multi-bit subtraction operation.

### 7. Multiplexer and Demultiplexer

A multiplexer (MUX) is a combinational circuit that selects binary information from one of many input lines and directs it to a single output line. Selection of a particular input line is controlled by a set of selection lines. Conversely, a demultiplexer (DEMUX) is a combinational circuit that performs the reverse operation of multiplexing. It takes a single input and routes it to one of several outputs.

### 8. Encoder and Decoder

An encoder is a combinational circuit that converts binary information from a set of inputs to a unique binary code at the output. A decoder is a combinational circuit that converts the binary information from a single input to multiple outputs.

### 9. Combinational and Sequential Circuits

Combinational circuits are defined as the time-independent circuits which do not depend upon previous inputs to generate any output are termed as combinational circuits. Sequential circuits are those which are dependent on clock cycles and depends on present as well as past inputs to generate any output.

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**Make sure to understand the concepts and definitions well. Try to draw out the circuits and truth tables for a clearer understanding. All the best for your VIVA!**