Page 1042 - The Mechatronics Handbook

TABLE 36.17 Functions of Two Variables Defined as Boolean Expressions
Name Expression Circuit Representation
0 ALWAYS 1 1 1
1 NEVER 0 0 0
2 1st Var a a a
3 2nd Var b - b b
4 NOT 1st Var a a - a
- -
5 NOT 2nd Var b V - b b
-
6 MIN-0/NOR ab = a ↓ b a a
b b
V - a
7 MIN-1 a b b
V - a
8 MIN-2 ab b
9 MIN-3/AND ab V a
b
∨
10 MAX-0/OR ab a
b
- a
∨
11 MAX-1 ab b
- a
∨
12 MAX-2 ab
b
- - a a
∨
13 MAX-3/NAND ab = a ↑ b b b
V - V - a
14 EXOR A b = ab ∨ ab b
15 COIN aΘb = a b a b
TABLE 36.18Truth Tables for Two Variable Functions
NOR AND OR NAND
a b m 0 m 1 m 2 m 3 M 0 M 1 M 2 M 3 XOR COIN a b a b LO HI
0 0 1 0 0 0 0 1 1 1 0 1 0 0 1 1 0 1
0 1 0 1 0 0 1 0 1 1 1 0 0 1 1 0 0 1
1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 1 0 1
1 1 0 0 0 1 1 1 1 0 0 1 1 1 0 0 0 1

by specialized symbols. The circuit symbols for the gates that perform functions of two independent
variables are shown in Table 36.17. The gates are identified by the adjective representing the operation
they perform. The most common gates are the AND, OR, NAND, NOR, XOR, and COIN gates. The
only nontrivial single input gate is the invertor or NOT gate. Gates are the basic elements from which
more complicated digital logic circuits are constructed.
A logic circuit whose steady-state outputs depend only on the present steady-state inputs (and not on
any prior inputs) is called a combinational logic circuit. To depend on previous inputs would require
memory, thus a combinational logic circuit has no memory elements.
Boolean algebra allows any combinational logic circuit to be constructed soley with AND, OR, and
NOT gates. Any combinational logic circuit may also be constructed solely with NAND gates, as well as
solely with NOR gates.

36.12 Expansion Forms

The sum of products (SP) is a basic form in which all boolean functions can be expressed. The product
of sums (PS) is another basic form in which all boolean functions can be expressed. An illustrative
example is given in Figs. 36.4(b,c) for the example given in Fig. 36.4(a).

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