Monday, December 24, 2012

Combinations of Gates

Combinations of Gates

Very often it is convenient to be able to perform a logical function using a different kind of gate.

AND Followed by NOT

If an AND gate is followed by a NOT gate (see Fig.12) the output of the circuit will be Combinations of Gates10. Therefore, the combination acts like a NAND gate.

Combinations of Gates3

 

Combinations of Gates6

Combinations of Gates1

AND Preceded by NOT

If all of the inputs to an AND gate are inverted, see Fig .13, the output of the circuit will be F = Ā.Ḃ. The truth table for this equation is given by Table 8.10. If this table is compared with the truth tables of the various gates it will be seen that the NOR logical function has been performed.

Combinations of Gates2

Therefore,

Combinations of Gates4

Similarly

Combinations of Gates5

Combinations of Gates7

NAND Preceded by NOT

The truth table for the circuit of Fig. 14 is given by Table 11. This shows that the output of the circuit is 1 whenever any one, or

Combinations of Gates12

Combinations of Gates

more, of its inputs is at 1. This means that the circuit performs the OR logical function. The Boolean expression for the circuit is

Combinations of Gates13

NAND Followed by NOT

When a NAND gate is followed by a NOT gate, Fig. 15, the AND function is performed.

Combinations of Gates1_13

OR Followed by NOT

Fig .16 shows a 2-input OR gate that is followed by a NOT gate. The combination acts like a NOR gate.

Combinations of Gates1_16

OR Preceded by NOT

Combinations of Gates16

Fig .17 shows a 2-input OR gate that has both of its inputs fed via NOT gales. Table 12 gives the truth table of the circuit and shows that the circuit performs the logical function NAND. The Boolean expression describing the circuit is given by equation (8.18), i.e.

Combinations of Gates15

Combinational Logic Circuits2_09

NOR Followed by NOT

Combinations of Gates17

NOR Preceded by NOT

Fig. 19 shows a NOR gate both of whose inputs are passed through a NOT gate. The truth table of the arrangement is given by Table 13. The output of the circuit is at logical 1 only when both of its inputs are at logical 1. Hence, the circuit performs the AND logical function. The Boolean expression for the circuit is given by equation (8.19). i.e.

Combinations of Gates14

Combinational Logic Circuits

The basic logic gates are used in combination to form other, more complex, logical functions. These logic functions are formed by suitably inter-connecting the individual gates

3_03

. Some of the functions that may be required can also be obtained 'ready-made', as it were, in an SSI package. Logic functions can also be generated using LSI circuits known as ROMs and PLDs but only the use of the basic will be considered here.