Combinations of Logic Gates

Truth tables can be used to work out the function of a combination of gates.

For example the truth table below shows the intermediate outputs D and E as well as the final output Q for the system shown below.

Inputs Outputs A B C D E Q 0 0 0 1 0 1 0 0 1 1 0 1 0 1 0 0 0 0 0 1 1 0 1 1 1 0 0 0 0 0 1 0 1 0 0 0 1 1 0 0 0 0 1 1 1 0 1 1

D = NOT (A OR B)
E = B AND C
Q = D OR E = (NOT (A OR B)) OR (B AND C)

Substituting one Type of Gate for Another - NAND Synthesis

Logic gates are available on ICs which usually contain several gates of the same type, for example four 2-input NAND gates or three 3-input NAND gates. This can be wasteful if only a few gates are required unless they are all the same type. To avoid using too many ICs you can reduce the number of gate inputs or substitute one type of gate for another. NAND gates can be combined to create any type of gate. This enables a circuit to be built from just one type of gate.

The table below shows the NAND gate equivalents of NOT, AND, OR and NOR gates.

GATE		Equivalent in NAND gates
NOT
AND
OR
NOR

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