LOGIC GATE In Digital Systems

LOGIC GATES

A gate is a logic component that has one or more input signals but produces only one output signal. The output and input are digital signals with two conditions, logic 1 and logic 0.

AND Gate

The AND Gate has two or more input signals but only one output signal. The output signal will be logic 1 if all inputs are logic 1.
Symbol is given in Figure 1 and  Truths Table is given in Table 1

Figure 1   AND Gate

 Table  1   The truth table of AND gates

Att any input can be given the data (0 or 1) and generate an output based on truth table above. Figure 2 shows a functional timing diagram of an AND gate with inputs A and B and outputs F.

Figure 2    Time diagram of an AND gate

The logical nature of the AND gate is the same as in the series switch circuit in Figure 3, the LED will light up only when both switches are closed.

Figure 3    The series switch circuit

AND Gate can have up to 8 inputs, AND with 3 inputs is given in Figure 4, and the truth table is given in Table 2.


Figure 4     AND Gate with 3 inputs

 

Table 2    AND Gate truth table 3 inputs

Application example, in the practical use IC 7408 which consists of 4 AND gates, one of which is connected to an LED to test the correctness of its logic. The LED will light up only when both inputs are supplied with 5V voltage. If one of the inputs is connected to ground (logic 0) then the LED will go out. The full test is given in Table 3.

 

Figure 5   AND gate test results

Table 3    AND gate test results Truth Table

 

OR  Gate

An OR gate has two or more input signals and one output signal. If one of the inputs is high, then the output signal is high. If all inputs are high then the output will be low. Figure 6 is the symbol and Table 4 is the truth table.

Figure 6    OR Gate

Table 4    OR Gate True Table

The logic properties are the same as in a parallel switch circuit which is inversely related to the AND gate properties. Look at Figure 7, the LED will light up when one of the switches is closed.

Figure 7    Parallel switch circuit

Figure 8   OR gate timing diagram

 

In Figure 8  the timing diagram of the OR gate is given when inputs A and B are given arbitrary signals and the signal shape is obtained at output F based on the truth table in Table 4.

OR gates can have up to 8 inputs, OR with 3 inputs is given in Figure 9 with the correct table in Table 5.

Figure 9    OR  3 inputs

Table 5   True table OR 3 inputs

Application example.

The TTL 7432 IC consists of 4 OR gates, one of which is arranged to turn on the LED as shown in Figure 10. The LED will light up as long as there is a voltage on one of its inputs.

Table 6   OR gate test results

Figure 10   Circuit OR Gate Test

 

NOT Gate

NOT gate is a gate with one input signal and one output signal. The output state is always opposite to the input state so it is often called an inverting gate (Inverter). The symbols for these gates are given in Figure 11 and the logical truth table is given in Table 7.

 

Figure 11   NOT Gate

Table 7    Truth table NOT gate

 

Figure 12   Example NOT gate timing diagram

From Figure 12 it can be seen that the signal at the output F is an inversion of the signal entered at input A.

 

NAND Gate

The NAND gate has the inverse nature of the AND gate, having two or more input signals and one output signal. All inputs must be high to produce a low output, otherwise the output is high. The symbols for these gates are given in Figure 13 and the logical truth table is given in Table 8.

 

Figure 13.    NAND gate 2 inputs

Table 8   Table Truth NAND gate

NAND gates can be constructed from AND gates and NOT gates, where the output of the AND gate is inputted to the NOT gate as Figure 14.

Figure 14    NAND gate AND and NOT

Figure 15    Example of a NAND gate timing diagram

Figure 15 is an example of input data at inputs A, B, with the output F based on Table 8. It can be seen that the signal at output F will be logic 0 if both inputs A and B are logic 1.

 

NOR  Gate

The NOR gate (Not-OR) is the opposite of the OR gate, having two or more than two input signals and one output signal. To get a high output from this gate all inputs must be in a low state. The symbols for these gates are given in Figure 16 and the logical truth table is given in Table 9.

 

Figure 16     2 input NOR gate

Table 9    NOR gate truth table

NOR gates can be constructed from OR gates and NOT gates by connecting the output of the OR gate to the input NOT gate as in Figure 17.

Figure 17     NOR of OR and NOT Gates

 

XOR Gate

The EX-OR gate has two inputs and one output signal. The output will be high if the input is different logic. The function of this gate is given in Table 10 and its symbol is given in Figure 18

Figure 18. EX-OR Gate

Table 10   EX-OR . gate truth table

 

XNOR Gate

The EX-NOR gate is the opposite of the EX-NOR gate, having two input signals and one output signal. The output will be high if the input is the same logic. This gate can be made from EX-NOR gate with NOT gate. The symbols of these gates are given in Figure 19 and the logical truth table is given in Table 11.

Figure 19.     EX-NOR Gate

Table 11    Truth Table EX-NOR gate

 

Conclusion

  1. Logic gates are components in digital engineering, which work based on logic 1 or 0
  2. If an electronic system is assembled with gates logic is called a logic circuit.