Sep 082014
 

Logic AND gate

The logic AND gate is one of the simplest gates in Digital Electronics. The symbols for a 2 and a 3 input AND gates are shown in the following pictures. The first one is the symbol of a 2 input AND gate and the second one is the symbol of a 3 input AND gate.

Symbols of a 2 & 3 input logic AND gate

The 2 input logic AND gate is the most known, although it can have many more inputs (A, B, C, etc.), but it only has one output: X. Two input AND gate has the following truth table.

2 input logic AND gate truth table

Two input AND gate truth table

It is easy to see that the output X is “1” (logical 1, high level) when the input A and B are “1”. In other words, the output X will be “1” when A and B inputs are “1”. The AND gate is represented by Boolean algebra as: X = A*B or X = AB. A 3 input logic AND gate implemented with switches is shown in the following diagram.

3 input logic AND gate made with switches

Truth table of a 3 input logic AND gate.  O = Open and C = Closed

3 input logic AND gate truth table

A logic AND gate may have many inputs. We can create a multiple input AND gate connecting 2 inputs AND gates in cascade. The problem connecting AND gates in cascade is that the propagation time (time needed by the signal to travel from the input to the output) increases.

How to build a 3 input logic AND gate with 2 input AND gates

We can build a 3 inputs AND gate from 2 inputs AND gates in cascade as shown in the diagram below.

3 input logic AND gate made with 2 input AND gates

The truth table is similar to the one shown above, where switches are used.

3 input logic AND gate truth table

Using the same metod we can implement a 4 or more inputs logic AND gates.

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