Title: Digital System Fundamentals
1. Introduction
Digital System Fundamentals is a foundational area of study in electrical and computer engineering that
focuses on the principles and design of digital circuits. These systems process discrete signals (0s and 1s)
rather than continuous signals, enabling modern computing, communication, and control systems.
2. Number Systems
Digital systems operate using different number systems, especially binary. Understanding number systems is
essential for data representation and processing.
• Binary (Base-2): Uses digits 0 and 1.
• Decimal (Base-10): Commonly used by humans.
• Octal (Base-8) and Hexadecimal (Base-16): Used for compact binary representation.
• Conversions: Between these number systems are frequently needed in digital design.
• Signed Numbers: Representing negative numbers using methods like two’s complement.
3. Boolean Algebra and Logic Gates
Logic gates are the building blocks of digital circuits. Boolean algebra is used to describe and simplify logical
operations.
• Basic Gates: AND, OR, NOT
• Universal Gates: NAND, NOR
• Other Gates: XOR, XNOR
• Boolean Laws: Used to simplify expressions for efficient circuit design.
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• Karnaugh Maps (K-Maps): A visual method for logic minimization.
4. Combinational Logic Circuits
These circuits provide outputs based solely on the current inputs.
• Adders: Perform binary addition (Half Adder, Full Adder)
• Multiplexers (MUX): Select one input from many.
• Demultiplexers (DEMUX): Distribute a single input to multiple outputs.
• Encoders and Decoders: Convert data between formats.
• Comparators: Compare binary values.
5. Sequential Logic Circuits
Unlike combinational circuits, these depend on both current inputs and past states.
• Flip-Flops: Basic memory elements (SR, JK, D, T).
• Registers: Store multiple bits of data.
• Counters: Count pulses (asynchronous and synchronous).
• Clock Signals: Synchronize circuit operations.
6. Memory Elements
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Digital systems use memory to store data and instructions.
• RAM (Random Access Memory): Temporary storage, volatile.
• ROM (Read-Only Memory): Permanent storage.
• EEPROM: Electrically erasable programmable ROM.
7. Digital System Design
Designing digital systems involves combining logic elements into larger functional blocks.
• Finite State Machines (FSMs): Model systems with a limited number of defined states.
• Timing Diagrams: Show signal changes over time.
• Synchronous Design: Circuits that rely on a common clock signal.
8. Applications of Digital Systems
Digital systems are used in nearly all modern electronics:
• Computers and mobile devices
• Embedded systems (cars, appliances)
• Communication systems
• Robotics and automation
• Control systems
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9. Conclusion
Digital System Fundamentals provide the essential knowledge for designing, analyzing, and implementing
digital circuits. Mastery of this subject enables the creation of efficient, reliable, and scalable digital
technologies used in everyday life.
Questions
1. What is a Multiplexer?
A Multiplexer (MUX) is a combinational logic circuit that selects one of many input signals and forwards the
selected input to a single output line, based on control (select) inputs.
• It acts like a digital switch.
• For an n-to-1 multiplexer, there are:
• n input lines
• log₂(n) select lines
• 1 output line
Example: A 4-to-1 MUX has 4 inputs (I0–I3), 2 select lines (S0, S1), and 1 output (Y).
2. Design the Logic Circuit of 8-Input Multiplexer Using Sum of Products Logic
2.1 Truth Table of 8-to-1 Multiplexer
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S2
S1
S0
Output (Y)
I0
I1
I2
I3
I4
5
1
I5
I6
I7
2.2 Boolean Expression (Sum of Products)
We express the output Y as a function of the select inputs S2, S1, S0 and the data inputs I0–I7:
Y = \overline{S2}\overline{S1}\overline{S0} \cdot I0 + \overline{S2}\overline{S1}S0 \cdot I1 +
\overline{S2}S1\overline{S0} \cdot I2 + \overline{S2}S1S0 \cdot I3 + \\
S2\overline{S1}\overline{S0} \cdot I4 + S2\overline{S1}S0 \cdot I5 + S2S1\overline{S0} \cdot I6 + S2S1S0
\cdot I7
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⸻
2.3 Logic Diagram (Using Basic Logic Gates)
The logic circuit is made up of:
• 8 AND gates: each one ANDs one data input with the corresponding combination of select lines (with
inverters where needed).
• 1 OR gate with 8 inputs to combine the outputs of the AND gates.
• NOT gates to generate the complements of select inputs.
Diagram Components:
• Inputs: S2, S1, S0 (select), I0–I7 (data)
• Gates: 8 ANDs, 3 NOTs, 1 OR
(If you’d like, I can provide an actual logic diagram image.)
3. What is the Purpose of a Magnitude Comparator?
A Magnitude Comparator is a combinational circuit used to compare two binary numbers (say A and B) and
determine their relative magnitude.
It gives three outputs:
•A>B
•A=B
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•A<B
Purpose:
• Used in digital systems for sorting, decision-making, and arithmetic operations.
• Essential in ALUs, digital counters, and control units.
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