组合逻辑分析 Combinational Logic Analysis

Basic Combinational Logic Circuits

The features of combinational logic:

• The output at current depends on the combination of inputs at current.
• The circuit has neither storage nor feedback.

This section includes:

• AND-OR Logic.
• AND-OR-Invert Logic
• Exclusive-OR Logic
• Exclusive-NOR Logic

AND-OR Logic

AND-OR logic can directly implement combinational logic circuits in the sum-of-products (SOP) form.

AND-OR-Invert Logic

AND-OR-Invert logic (AOI) is the inverse of the output of an SOP expression. $\Rightarrow$ POS.

Exclusive-OR Logic

The output is HIGH whenever the two inputs are different.


$X=A\overline{B}+\overline{A}B \quad X=A \oplus B$

Exclusive-NOR Logic

The output is HIGH whenever the two inputs are the same.

Procedures of Analyzing Combinational Logic

1. Write down the Boolean expression.
2. Simplification.
3. The function is …

Implementing Combinational Logic

Implementing an SOP expression is done by first forming the AND terms; and then ORing the terms together.

Implementing a truth table can be done by first writing the SOP expression; and then implementing the expression.

The Universal Property of NAND and NOR Gates

Dual Symbols, Bubble Cancellation.

Combinational Logic Using NAND and NOR Gates

逻辑门的等价性。

Pulse Waveform Operation