T HE NOT F UNCTION

T HE NOT F UNCTION

Figure 3-5 illustrates the NOT symbol, which is used to graphically represent the NOT function. The NOT output is TRUE (1) if the input is FALSE (0). Conversely, if the output is FALSE (0), the input is TRUE (1). The result of the NOT operation is always the inverse of the input; therefore, it is sometimes called an inverter.

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S ECTION Introductory Logic C HAPTER 1 Concepts

Concepts 3

The NOT function, unlike the AND and OR functions, can have only one input. It is seldom used alone, but rather in conjunction with an AND or an OR gate. Figure 3-6 shows the NOT operation and its truth table. Note that an A with a bar on top represents NOT A.

Input

Output

Figure 3-5. Symbol for the NOT function.

NOT Truth Table

NOT

Figure 3-6. NOT gate and its truth table.

At first glance, it is not as easy to visualize the application of the NOT function as it is the AND and OR functions. However, a closer examination of the NOT function shows it to be simple and quite useful. At this point, it is helpful to recall three points that we have discussed:

1. Assigning a 1 or 0 to a condition is arbitrary.

2. A 1 is normally associated with TRUE, HIGH, ON, etc.

3. A 0 is normally associated with FALSE, LOW, OFF, etc. Examining statements 2 and 3 shows that logic 1 is normally expected to

activate some device (e.g., if Y = 1, then motor runs), and logic 0 is normally expected to deactivate some device (e.g., if Y = 0, then motor stops). If these conventions were reversed, such that logic 0 was expected to activate some device (e.g., if Y = 0, then motor runs) and logic 1 was expected to deactivate some device (e.g., Y = 1, then motor stops), the NOT function would then have

a useful application.

1. A NOT is used when a 0 (LOW condition) must activate some device.

2. A NOT is used when a 1 (HIGH condition) must deactivate some

device. The following two examples show applications of the NOT function.

Although the NOT function is normally used in conjunction with the AND and OR functions, the first example shows the NOT function used alone.

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S ECTION Introductory Logic C HAPTER 1 Concepts

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E X AM PLE 3 -3

Show the logic gate, truth table, and circuit representation for a solenoid valve (V1) that will be open (ON) if selector switch S1 is ON and if level switch L1 is NOT ON (liquid has not reached level).

S OLU T I ON

V1 S1

Level Switch L1

S1 V1

L1

Logic Representation

V1

S1

L1 (L1)

Truth Table

CR1-1

S1

Electrical Ladder Circuit

Note: In this example, the level switch L1 is normally open, but it closes when the liquid level reaches L1. The ladder circuit requires an auxiliary control relay (CR1) to implement the not normally open L1 signal. When L1 closes (ON), CR1 is energized, thus opening the normally closed CR1-1 contacts and deactivating V1. S1 is ON when the system operation is enabled.

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S ECTION Introductory Logic C HAPTER 1 Concepts

Concepts 3

E X AM PLE 3 -4

Show the logic gate, truth table, and circuit representation for an alarm horn that will sound if push button PB1 is 1 (ON or depressed) and PB2 is NOT 0 (not depressed).

S OLU T I ON

PB1

Alarm Horn

PB2

Logic Representation

Electrical Circuit

Line Voltage

Line Voltage (Common)

Electrical Ladder Circuit

Note: In this example, the physical representation of a field device element that signifies the NOT function is represented as a normally closed, or not normally open, switch (PB2). In the logical representation section of this example, the push button switch is represented as NOT open by the

symbol.

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S ECTION Introductory Logic C HAPTER 1 Concepts

Concepts 3

The two previous examples showed the NOT symbol placed at inputs to a gate. A NOT symbol placed at the output of an AND gate will negate, or invert, the normal output result. A negated AND gate is called a NAND gate. Figure 3-7 shows its logic symbol and truth table.

N NAND Truth Table A N D T r u t h T a b l e

Figure 3-7. Two-input NAND gate

and its truth table.

The same principle applies if a NOT symbol is placed at the output of an OR gate. The normal output is negated, and the function is referred to as a NOR gate. Figure 3-8 shows its symbol and truth table.

N NOR Truth Table O R T r u t h T a b l e

Figure 3-8. Two-input NOR gate

and its truth table.