2-6THE AND GATEThe AND gate is a logic circuit that requires all inputs to be TRUE at the same time in order for theoutput to be TRUE.LOGIC SYMBOLThe standard symbol for the AND gate is shown in figure 2-2. Variations of this standard symbolmay be encountered. These variations become necessary to illustrate that an AND gate may have morethan one input.Figure 2-2. —AND gate.If we apply two variables, A and B, to the inputs of the AND gate, then both A and B would have tobe TRUE at the same time to produce the desired TRUE output. . The symbol f designates the outputfunction. The Boolean expression for this operation is f = A·B or f = AB. The expression is spoken, "f =A AND B." The dot, or lack of, indicates the AND function.AND GATE OPERATIONWe can demonstrate the operation of the AND gate with a simple circuit that has two switches inseries as shown in figure 2-3. You can see that both switches would have to be closed at the same time tolight the lamp (view A). Any other combination of switch positions (view B) would result in an opencircuit and the lamp would not light (logic 0).Figure 2-3.—AND gate equivalent circuit: A. Logic 1 state; B. Logic 0 state.Now look at figure 2-4. Signal A is applied to one input of the AND gate and signal B to the other.At time T_{0}, both inputs are LOW (logic 0) and f is LOW. At T_{1}, A goes HIGH (logic 1); B remains LOW;and as a result, f remains LOW. At T_{2}, A goes LOW and B goes HIGH; f, however, is still LOW, becausethe proper input conditions have not been satisfied (A and B both HIGH at the same time). At T_{4}, both A