Analysis of Combinational Logic Circuits

The purpose of analyzing combinational logic circuits is to determine the logical function of a known circuit. The steps are as follows:
1. Write the logical expressions of each output terminal from the logic diagram;
2. Simplify and transform each logical expression
3. List the truth table
4. Analyze the logic circuit based on the truth table and logical expression, and finally determine its function.
The following example illustrates the analysis method of combinational logic circuits.

Example: Given a logic circuit as shown below, analyze the function of the circuit.

Solution: Step 1, based on the logic diagram, the logical expression of the output function can be written as

Step 2, write the truth table as follows:

A B C L 0 0 0 0 1 1 1 1 0 0 1 1 0 0 1 1 0 1 0 1 0 1 0 1 0 0 1 1 1 1 0 0 0 1 1 0 1 0 0 1

The third step is to analyze the truth table and know that when there is an odd number of 1s in the input variables A, B, and C, L is 1, otherwise L is 0. It can be seen that this circuit can be used to check the parity of a 3-bit binary code. Since it outputs a valid signal when the input binary code contains an odd number of 1s
, it is called an odd-check circuit.

Example: A combinational logic circuit with two inputs and two outputs is shown in the figure below. Analyze the function of this circuit.

Solution: The first step is to write the logical expression from the logic diagram, and simplify and transform it:

The second step is to write the truth table as follows:

enter Output A B S C ０ ０ １ １ ０ １ ０ １ ０ １ １ ０ ０ ０ ０ １

The third step is to analyze the truth table. When A and B are both 0, S is 0 and C is also 0
; when one of A and B is 1, S is 1 and C is 0; when A and B are both 1, S is 0 and C is 1. This is in line with the principle of adding two 1-bit binary numbers, that is, A and B are two addends, S is their sum, and C is the carry to the higher bit. This circuit can be used to add two 1-bit binary numbers. In fact, it is the basic unit circuit in the operator, called a half adder.
For relatively simple combinational logic circuits, the method of drawing waveforms can sometimes be used for analysis. In order to avoid mistakes, the output waveform is usually drawn step by step based on the input waveform, and finally the function is determined based on the relationship between the output and input waveforms of the logic diagram. The analysis results of the above two examples using the analysis method of drawing waveforms are shown in the following figures.