276 DIGITAL BUILDING BLOCKS AND COMPUTER SYSTEMS
truth table. Similarly, the OR operation followed by the NOT operation is known as the NOR
operation. Figure 6.1.5 shows a typical NOR gate with its truth table.
Two other logic blocks that are sometimes used are the EXCLUSIVE OR (XOR) and
EXCLUSIVE NOR (COINCIDENCE) gates. Their conventional symbols together with their
truth tables are shown in Figures 6.1.6 and 6.1.7, respectively. It is also possible to synthesize
these logic blocks by combining the basic OR, AND, as well as NOT logic gates.
The operations so far introduced are summarized in Table 6.1.2. Any Boolean function can
be transformed from an algebraic expression into a combinational network by using the basic
logic gates. It is always desirable, however, to implement a given Boolean function by using the
minimumnumber of components, leading to a less complex and more economical network. Table
6.1.3 gives the basic Boolean identities for which the truth tables for the expressions on either
side of the equals sign are the same. The reader should note that, in general, it is improper to draw
a diagram in which the outputs of any two blocks are connected together. Two outputs can be
combined by using them as two inputs to another gate.AAB10
10
11
11F0
0
0
000
00
01
01C0
1
0
10
1
0
11
0
0
0F = A + B + C
C
(a) (b)Inputs OutputBFigure 6.1.5NOR gate.(a)Logic
symbol.(b)Truth table.AAB
00
01
10
11F
0
1
1
F = A ⊕ B 0
B F = A ⋅ B + A ⋅ B
(a) (b)Inputs OutputFigure 6.1.6EXCLUSIVE OR gate (XOR) (also known as binary
comparator).(a)Logic symbol.(b)Truth table. NOTE: XOR operation
yields 1 if the inputAis1orBis 1, but yields 0 if both inputsAandB
are1or0.AAB
00
01
10
11F
1
0
0
F = A B 1
B F = A ⋅ B + A ⋅ B
(a) (b)Inputs OutputFigure 6.1.7EXCLUSIVE NOR gate (COINCIDENCE) (also known
as XNOR or EQUIVALENT gate).(a)Logic symbol.(b)Truth table.
NOTE: XNOR operation yields 1 if both inputsAandBhave the same
value of either 0 or 1, but yields 0 if the inputAis1orBis 1. Hence it
is a complement of XOR gate.