Combining Logic Gates
Combining Logic Gates

### Chapter Overview

Earlier you memorized the symbol, truth table, and Boolean expression for each logic gate. These gates are the building blocks for more complicated digital devices. In this chapter you will use your knowledge of gate symbols, truth tables, and Boolean expressions to solve real-world problems in electronics.

You will be connecting gates to form what engineers refer to as combinational logic circuits. By deﬁnition, combinational logic is an interconnection of logic gates to generate a speciﬁed logic function where the inputs result in an immediate output; hav¬ing no memory or storage capabilities. This is also sometimes called combinatorial logic. Digital circuits that have a memory or storage capability are called sequential logic circuits and will be studied later.

You will be combining gates (ANDs, ORs) and inverters to solve logic problems that do not require memory. The “tools of the trade” for solving combinational logic problems are: truth tables, Boolean expres¬sions, and logic symbols. Do you know your truth tables, Boolean expressions, and logic symbols? An understanding of com¬bination logic is knowledge required of all who work as a technician, troubleshooter, designer, or engineer in electronics.

To gain maximum experience you should try to implement your combinational logic circuits in hardware in the laboratory. Logic gates are packaged in inexpensive, easy-to-use integrated circuits (ICs). Also, your com¬binational logic circuits can be tested using circuit simulation software on your computer.

Solve combinational logic problems with programming. Try programming a simple programmable logic device such as an inexpensive PAL or GAL if your lab has PLD programming equipment. Finally, solve real-world combinational logic functions by programming a microcontroller using a PC and the BASIC Stamp 2 module.

1. Draw logic diagrams from minterm and maxterm Boolean expressions.
2. Design a logic diagram from a truth table by ﬁrst developing a minterm Boolean expression and then drawing the AND-OR logic diagram.
3. Reduce a minterm Boolean expression to its simplest form using two-, three-, four-, and ﬁve-variable Karnaugh maps.
4. Simplify AND-OR logic circuits using NAND gates.
5. Convert back and forth from Boolean expression to truth table to logic symbol diagram using computer simulation (such as the Logic Converter instrument from Electronic Workbench® or MultiSIM®).
6. Solve logic problems using data selectors.
7. Understand the fundamentals of selected programmable logic devices (PLDs).
8. Convert minterm-to-maxterm and maxterm-to-minterm Boolean expressions using De Morgan’s theorems.
9. Use a “keyboard version” of Boolean expressions.
10. Program several logic functions using a BASIC Stamp microcontroller module.

### Study Outline

 4-1 Constructing Circuits from Boolean Expressions (See page(s) 84) 4-2 Drawing a Circuit from a Maxterm Boolean Expression (See page(s) 85) 4-3 Truth Tables and Boolean Expressions (See page(s) 86) 4-4 Sample Problem (See page(s) 89) 4-5 Simplifying Boolean Expressions (See page(s) 92) 4-6 Karnaugh Maps (See page(s) 93) 4-7 Karnaugh Maps with Three Variables (See page(s) 94) 4-8 Karnaugh Maps with Four Variables (See page(s) 95) 4-9 More Karnaugh Maps (See page(s) 96) 4-10 A Five-Variable Karnaugh Map (See page(s) 98) 4-11 Using NAND Logic (See page(s) 99) 4-12 Computer Simulations-Logic Converter (See page(s) 100) 4-13 Solving Logic Problems—Data Selectors (See page(s) 104) 4-14 More Data Selector Problems (See page(s) 107) 4-15 Programmable Logic Devices (PLDs) (See page(s) 110) 4-16 Using DeMorgan’s Theorems (See page(s) 118) 4-17 Solving a Logic Problem (BASIC Stamp Module) (See page(s) 121)