Combinational logic

Combinational logic

Often quite a large number of gates are used to solve a particular problem. When used together they make up a combinational logic circuit. You can use any of the fives gates to solve such a logic problem. In many circuits the NAND gate is used as the basic
‘building block’. All the other gates mentioned can be made up from NAND gates. Fig. 45.24 shows the simplest of these, the NOT gate or inverter. Here the two NAND gate inputs are linked together to make’ one input. If this input is I the output is O-and vice versa.

A NAND gate as an inverter
A NAND gate as an inverter

Fig. 45.25 (a) shows two NOT gates and a NAND gate, linked. NAND gates could be used as the two inverters or NOTs. A full truth table for the system is also shown. This table shows how to work out what this system does. Two middle points, X and Y, are labelled as well as the inputs and outputs.
The A and B columns are as usual for a 2-input gate. The X column is the opposite of A, since there is a NOT gate between them. The Y column is the opposite ofB. The voltage signals at X and Yare fed into a NAND gate. The resulting OUT column shows that these three gates make up an OR gate.

More complex logic gate circuits
More complex logic gate circuits

In the circuit in Fig. 45.25 (b), three different gates are shown in combination. The final truth table is found in the same way as for (a), by identifying the intermediate points in the layout. In this case there are two such points. The resulting logic state at each is found by considering the inputs to a gate and the truth table of the relevant gate. So X is simply NOT A-the X values are the opposite of the A values. Then Y is the result of linking X and B into an OR gate. The value ofY will be I if X OR B is 1. Finally the OUTPUT is the result Y into a NOT gate. The result is not one of the five standard gates. This truth table can only be achieved by combining several standard gates.

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