2.Digital Design with CPLD Applications _ VHDL - Dueck

28 CHAPTER 2 • Logic Functions and Gates
FIGURE 2.2
2-Input AND Gate Symbols
Algebraically, this is written:
Y A B
Pronounce this expression “Y equals A AND B.” The AND function is similar to multiplication
in linear algebra and thus is sometimes called the logical product. The dot between
variables may or may not be written, so it is equally correct to write Y AB. The
logic circuit symbol for an AND gate is shown in Figure 2.2 in both distinctive-shape and
IEEE/ANSI rectangular-outline form. The qualifying symbol in IEEE/ANSI notation is the
ampersand (&).
We can also represent the AND function as a set of switches in series, as shown in Figure
2.3. The circuit consists of a voltage source, a lamp, and two series switches. The lamp
turns on when switches A AND B are both closed. For any other condition of the switches,
the lamp is off.
Voltage
source
A
A
B
B
Lamp
FIGURE 2.3
AND Function Represented by Switches
Table 2.3 3-input AND
Function Truth Table
A B C Y
0 0 0 0
0 0 1 0
0 1 0 0
0 1 1 0
1 0 0 0
1 0 1 0
1 1 0 0
1 1 1 1
Table 2.3 shows the truth table for a 3-input AND function. Each of the three inputs
can have two different values, which means the inputs can be combined in 2 3 8 different
ways. In general, n binary (i.e., two-valued) variables can be combined in 2 n ways.
Figure 2.4 shows the logic symbols for the device. The output is HIGH only when all
inputs are HIGH.
FIGURE 2.4
3-Input AND Gate Symbols
OR Function
Table 2.4 2-input OR
Function Truth Table
A B Y
0 0 0
0 1 1
1 0 1
1 1 1
KEY TERMS
OR gate A logic circuit whose output is HIGH when at least one input (e.g., A
OR B OR C) is HIGH.
Logical sum OR function.
The OR function combines two or more input variables in such a way as to make the output
variable HIGH if at least one input is HIGH. Table 2.4 gives the truth table for the 2-input
OR function.