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MindMap Gallery Basics of digital electronics technology (combinational logic circuits)

Basics of digital electronics technology (combinational logic circuits)

"A Concise Tutorial on the Basics of Digital Electronic Technology" by Tsinghua University. Yu Mengchang. The fourth edition (Chapter 4 Combinational Logic Circuits) has a detailed introduction and comprehensive description. I hope it can help interested friends learn.

Edited at 2023-11-30 19:32:19

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Basics of digital electronics technology (combinational logic circuits)

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Outline

Chapter 4 Combinational Logic Circuits
- 25
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Combinational logic circuit module design
- 33
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Basics of digital electronic technology (sequential logic circuits)
- 49
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Fundamentals of digital electronics technology (flip-flops)
- 79
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Basics of digital electronic technology (gate circuits) mind map
- 56
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Digital Electronics Technology Basics

Chapter 4 Combinational Logic Circuits

Overview

1 Characteristics of combinational logic functions

Logic function characteristics: The output state of the circuit at any moment only depends on the input state at that moment, and has nothing to do with the original state.

Circuit structure characteristics

①There is no feedback delay circuit between output and input

②Does not contain memory components (flip-flops) and consists only of gate circuits

2. Representation method of logic function of combinational circuit

Truth tables, Karnaugh maps, logical expressions, waveform diagrams, etc., can all be used to represent the logical functions of combinational circuits.

3 Classification of Combinational Circuits

Different logic functions: adder, numerical comparator, encoder, decoder, data selector, data distributor, read-only memory

Different switching components: CMOS, TTL

According to different levels of integration: SSI, MSI, LSI, VLSI

4.1 Basic analysis methods and design methods of combinational circuits

1 Analysis method

step:

2 Design methods

step:

4.2 Adder

Arithmetic operations on binary numbers

Refer to Chapter 1 for base conversion

Half adder: Add two 1-bit binary numbers without considering low-bit carry

Truth table:

Functional form:

National standard symbol:

Full adder: Two addends with the same bit and a carry from the low bit are added together. This addition operation is a full add.

Truth table:

Functional form:

National standard symbol:

Integrated full adder (dual full adder)

TTL:

CMOS:

Adder: A circuit that adds multi-bit binary numbers

Arithmetic formula:

4-bit serial carry adder

Features: The circuit is simple, but the computing speed is not high

Connection Diagram:

carry lookahead adder

Definition: When doing addition, the carry signal of each digit is directly generated by the input binary number.

Features: Fast, but complex circuit

Connection Diagram:

4.3 Encoders and decoders

Coding system: A method of using multiple digits to represent information about different things according to certain rules.

Encoder

Binary encoder:

Three-digit binary encoder (8-wire-3-wire encoder)

Schematic block diagram:

Coding table:

Features:

three-digit binary priority encoder

Coding table:

Features: Priority encoding, which allows several signals to be input at the same time, but only encodes the signal with the highest priority

Integrated 8-wire-3-wire priority encoder

Coding table:

Two 8-line-3-line priority encoders are cascaded into one 16-line-4-line priority encoder Three 8-line-3-line priority encoders are cascaded into one 24-line-5-line priority encoder Four 8-line-3-line priority encoders are cascaded into one 32-line-5-line priority encoder

Binary-decimal encoder: encodes ten signals from 0 to 9 using 4-bit binary codes

8421BCD code encoder (10-4 lines encoder)

Schematic block diagram:

Coding table:

8421BCD code priority encoder

Coding table:

decoder

Binary decoder: a circuit that translates the various states of binary codes into corresponding output signals according to their original meaning.

Features: The output terminal provides all minimum terms

Device examples

Integrated 3-wire to 8-wire decoder:

Device:

Input strobe control terminal:

Truth table:

Binary decoder cascade

Two 3-line to 8-line decoders are connected to form a 4-line to 16-line decoder.

Device:

Three pieces of 3-line to 8-line decoders are connected to form a 5-line to 24-line decoder.

Device:

Truth table:

Integrated 2-wire to 4-wire decoder

Function diagram:

Truth table:

Implementing combinational logic functions using binary decoders

Since the output of the binary decoder can provide all the minterms of the input variables, and any combinational logic function can be transformed into the standard formula of the sum of the minterms, any combinational logic function can be implemented using a binary decoder and a gate circuit

Binary-decimal decoder: a circuit that translates the binary code of decimal numbers, that is, the BCD code, into the corresponding 10 output signals

8421BCD code decoder

Display decoder: Translate the binary codes of numbers, words and symbols into the form that people are accustomed to and display them

digital display

display decoder

4.4 Data selectors and allocators

Data selector: A circuit that selects one output from multiple inputs

Letter representation

D is the data input terminal

A is the address input terminal

For the strobe control terminal

Y is the data output terminal

Integrated 4-to-1 data selector

Device:

Truth table:

Integrated 8-to-1 data selector

Device:

Truth table:

Integrated data selector extension

Data distributor: a circuit that transmits multiple outputs from one input

1-way to 4-way data distributor

Schematic block diagram:

Truth table:

Integrated 1-channel to 8-channel data distributor

Implemented using a 3-wire to 8-wire decoder

Device:

4.5 Parity checker and numerical comparator

Parity checker: Using the logic function of the XOR gate, parity check operations can be performed

If the output is 0, then the number of 1's in the input is an even number. If the output is 1, then the number of 1's in the input is an odd number.

Numeric comparator

In digital circuits, the input of a numerical comparator is the binary number to be compared, and the output is the result of the comparison.

1-bit numerical comparator

Schematic block diagram:

Truth table:

4-bit numerical comparator

Comparison starts from the high bit and proceeds bit by bit until the comparison result is obtained.

Schematic block diagram:

Truth table:

4.6 Implementing combinational logic functions using medium-scale integrated circuits

1 Use data selectors to implement combinational logic functions

step:

1 Select the data selector: determined by n=k-1 (k is the number of variables in the function, n is the number of selector address codes)

2. Write standard AND or expressions of functions

3 Compare and determine the expression of the input quantity

4. Draw a connection diagram

Example:

2 Use binary decoder to implement combinational logic function

step:

1 Select the decoder: 2 variables use a 2-4 line decoder, 3 variables use a 3 line-8 line decoder

2. Write the standard NAND-NAND form of functions

3 Confirm the relationship between variables and inputs

4. Draw a connection diagram

Example:

4.7 Read-only memory

Sort by writing method

Mask ROM

Programmable ROM

Erasable programmable ROM

ROM structure

4.8 Competitive Adventures in Combinational Circuits

Concept: In a combinational circuit, when the input signal changes state, a false signal may appear at the output - the phenomenon of excessive interference with the pulse is called contention risk.

The relationship between competition and risk-taking

Where competition does not necessarily lead to risk taking, where there is risk there must be competition.

Ways to eliminate competitive risk

①Introduction of blocking pulse

②Introduce strobe pulse

③Connect the filter capacitor

④Modify the logic design and add redundant items