Overview

In this course we mainly learned about:

• Logic Algebra: Basic Operations and Logic Function
• Combinational Logic Circuit: Encoder, Decoder, Adder
• Semiconductor Storage Circuit: SR Latch and Flip-Flops

一、Logic Algebra

Logic algebra is the foundation of digital circuits.

1. Basic Operations

There are three basic operations in logical algebra: AND, OR, and NOT.

​ AND: Y = A · B

​ OR: Y = A + B

​ NOT: Y = A’

We can use three graphics to represent them:

Below the symbols are truth table. We use them to list all possible input and output results.

Compound logic operations include NAND, NOR, etc.

2. Logic Function and Karnaugh Map

If the logic variable is input and the result is output, then the output depends on the input. Therefore, there is a functional relationship between input and output.

This functional relationship is called a logic function.

​ Y=F(A,B,C,···)

Karnaugh map is used to simplify logical functions. Example:

二、Combinational Logic Circuit

In a combinational logic circuit, the output at any time depends only on the input at that time, and has nothing to do with the original state of the circuit.

We mainly learned about some commonly used modules:

1) Encoder

The function of the encoder is to encode each input high and low level signal into a corresponding binary code.

For example, a 3-bit binary encoder, if the input is 10000000, the output can be 000

The common 8-3 priority encoder chip is 74HC148.

2) Decoder

The function of the decoder is to translate each input binary code into the corresponding output high and low level signals.

74LS138 is a commonly used 3-8 decoder chip.

3) Adder

The adder is responsible for the add operation.

There are two types of adder: half adder and full adder.

The half adder does not consider the carry C.

三、Semiconductor Storage Circuit

1) SR Latch

The SR latch is the most basic and simplest type of circuit structure among static memory cells.

2) Flip-Flop

The difference from the latch is that the flip-flop has an additional trigger signal input CLK.

Only when the trigger signal comes, the trigger can be set to the corresponding state according to the input.

There are many types of flip-flops.

• JK
• D
• T