Digital Logic, Electronics, and Communication Systems
Number Systems and Binary Arithmetic
Number systems are based on different radices: Decimal (base 10, digits 0–9), Binary (base 2, digits 0 and 1), Octal (base 8, digits 0–7), and Hexadecimal (base 16, digits 0–9 and A–F). Conversion is very important:
- To convert decimal to binary, repeatedly divide by 2 and write remainders in reverse order.
- To convert binary to decimal, multiply each bit by powers of 2 and sum them.
- Binary to octal conversion is done by grouping bits in 3s.
- Binary to hexadecimal
Digital Logic Circuits and Boolean Minimization Techniques
Binary Adders and Subtractors
A Half Adder is a combinational logic circuit that adds two single-bit binary numbers. It produces two outputs: Sum (S) and Carry (C). It is called a ‘half’ adder because it cannot handle a carry from previous additions.
Logic Expressions for Adders
- Half Adder: Sum (S) = A XOR B; Carry (C) = A AND B (A·B)
- Full Adder: This is a combinational circuit that adds three one-bit binary numbers: A, B, and Carry-in (Cin). It produces two outputs: Sum (S) and Carry-out (Cout). Full
Digital Electronics Concepts: Binary, Logic Gates & Memory
1) Binary to Decimal Conversion
To convert a binary number to decimal, multiply each bit by its place value (2⁰, 2¹, 2², etc.) and then add the results.
Example: 1011₂ = (1×2³) + (0×2²) + (1×2¹) + (1×2⁰) = 8 + 0 + 2 + 1 = 11 (decimal).
✅ 2) Advantages of Universal Gates
Universal gates are NAND and NOR gates. Their advantage is that a any logical function can be implemented using just one type of gate. This simplifies design, reduces manufacturing cost, and increases flexibility in
Read MoreDigital Logic Circuits: Arithmetic, Data Selection, and Codes
Core Combinational Circuits and Digital Fundamentals
This section covers the core combinational circuits that form the backbone of digital systems. Mastery of their design, truth tables, and applications is essential for Unit III.
1. Arithmetic Circuits: Full Adder and Full Subtractor
These circuits perform the fundamental binary arithmetic operations.
A. Full Adder (FA)
A Full Adder is a combinational logic circuit that performs the addition of three single-bit binary numbers: two operands (A and B)
Read MoreFlip-Flop Conversion and Karnaugh Map Techniques
Flip-Flop Conversion: Steps and Examples
The goal of flip-flop conversion is to use an available flip-flop (the basic component you have) along with a combinational logic circuit to make the overall system behave like a required flip-flop (the target).
General Steps for Conversion
- Identify Available and Required FFs:
- Required FF (Target): The one you want to emulate (e.g., T-FF). Its inputs are the external inputs for the final circuit.
- Available FF (Source): The one you are using (e.g., JK-FF). Its
Combinational Logic Circuits: Demultiplexers, Decoders, Encoders, Comparators, and Converters
Combinational Logic Circuits Fundamentals
This document details several fundamental combinational logic circuits: Demultiplexers (DEMUX), Decoders, Encoders, Comparators, and Code Converters. These circuits perform data distribution, decoding, encoding, comparison, and conversion without using memory elements.
1. Demultiplexer (Data Distributor)
A Demultiplexer (DEMUX) is a combinational logic circuit that takes one input and distributes it to one of many output lines. The selection of the output line
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