Page 104 - Mechanical Engineers Reference Book

Analogue and digital electronics theory 2/45
1 BS3939 I IS0 I ;:$ I Inputs I Outputs
function
I C M T I Coffee 1 Tea

0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1

Figure 2.93 Truth table for drinks-vending machine

where C, T and M represent the coffee button, tea button and
money input, respectively, and the overbar represents the
inverse complement as usual.
Using De Morgan's theorem the system may alternatively
be written as
Coffee = (T + 72) + (T + T) (2.121)
Tea = T + R (2.122)
Thus the same logic system can be implemented using one OR
and three NOR gates, as shown in Figure 2.94.
The validity and equivalence of equations (2.119)-(2.122)
may easily be checked using a truth table. Four logic gates are
Figure 2.90 Gate symbol systems in current use again required but the circuit operates with inverted input
signals. This means that three inverters are also required in the
circuit as shown.
It is apparent that the logical function can be realized in
Coffee several different ways, e.g.
Coffee = (c + ii?) . (T + T) and Tea = TM
Using the above realization, the circuit takes the form shown
in Figure 2.95.
Tea
2.3.23 Logic systems using NAND and NOR gates
Figure 2.91 Logic circuit for drinks-vending machine only
Logic gates are packaged as arrays of the same type in IC
form. A typical example is SN7408, which is a 14-pin DIL
package containing four separate two-input AND gates.
Because the logic gates are marketed in this particular form it
is advantageous to design the logic circuit using only one type
of gate. This normally minimizes the number of IC packages
required. Figure 2.96 shows a two-input NAND gate driving
into a single-input NAND gate.

Tea
P
Figure 2.92 Extended logic circuit for drinks-vending machine

pressing either button on its own and satisfying the money
input criterion the correct drink will be output. The operation
of the e.utended system is verified in the truth table shown in
Figure 2.93. Tea
By ins,pection of Figure 2.92. the system can be represented
in Boolean expressions as
Coffee := (CM) . (CT (2.119) Figure 2.94 Logic circuit for drinks-vending machine using OR and
Tea = TM (2.120) NOR gates