Introduction to Industrial Automation

Figure 4.1  Switching elements and possible assignments of binary variables: (a) binary repre-

sentation of NO and NC relay contacts, (b) open contact as A = 0, (c) open contact as A = 1, 

(d) closed contact as A = 0, and (e) closed contact as A = 1.

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Logical Design of Automation Circuits 

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In general, a Boolean variable represents the level of voltage in a wire of a digital electronic circuit. 

Most commonly, the state with the high energy level is denoted as “1” or “high level” and the corre-

sponding one with the low energy level as “0” or as “low level”. In the typical digital electronic circuits 

(transistor–transistor logic or TTL circuits), the electrical voltage can take only two values: 0 V and +5 V, 

which are also presented in Figure 4.2 and, more especially, every electrical voltage below 0.4 V is 

equivalent to a “logical 0”, while every voltage above 2.4 V is equivalent to a “logical 1”.

In electrical circuits, the electrical components can be connected only in two ways, which is 

through series or parallel connections. The series connection of electrical components or switch-

ing contacts corresponds to the logical operation AND, while the parallel connection corresponds 

to the logical operation OR. These two operations, as well as the inversion operation, are imple-

mented with the help of the related logical gates AND, OR, and NOT.

A logical function Z = f(A, B, C,…) is a function where the independent variables A, B, C, … as 

well as the dependent variable Z all belong to the Boolean algebra. In a logical function, the three 

operations of Boolean algebra can exist together in a simple or complex form, or with variations 

of them. As we have seen in Chapter 3, automation circuits contain switching components that 

are connected in series, parallel, or in mixed connections, as well as through coils and relays. It 

can easily be concluded that these type of automation circuits can be straightforwardly described 

from an equivalent logical function. For example, consider the pushbutton shown in Figure 4.3a, 

where its contact is NO; the left connection terminal is considered to be under a voltage and thus 

equivalent to a logical 1. The activation or inactivation of the button can be described by the 

binary variable b, while the variable Z represents the voltage that exists in the right connection 

terminal. In this case, the following relationships can be extracted:

If b=0 (the button is not pressed) then Z=0 (there is no voltage).

If b=1 (the button is pressed) then Z=1 (there is voltage).

Thus, these two statements can result in the function Z=b, that can be considered as the describ-

ing function for an NO button. In a similar way, for the NC button shown in Figure 4.3b, the 

corresponding logical function is 

Z b

=

. Thus, all automation circuits can be approached indepen-

dently of their complexity. As a characteristic example, the circuit in Figure 3.1d, can be described 

by the logical function:

 

C STOP START C

=

+

⋅

(

),

where the STOP and the START labels can be considered as binary variables of the corresponding 

buttons.

t

0 V 

High level or logical 1 

5 V 

Low level or logical 0

Voltage