2-8The first combination (A = 0, B = 0) corresponds to T_{0} in figure 2-4; the second to T_{1}; the third to T_{2};and the last to T_{4}. When constructing a Truth Table, you must include all possible combinations of theinputs, including the all 0s combination.A Truth Table representing an AND gate with three inputs (X, Y, and Z) is shown below. Rememberthat the two-input AND gate has four possible combinations, with only one of those combinationsproviding a HIGH output. An AND gate with three inputs has eight possible combinations, again withonly one combination providing a HIGH output. Make sure you include all possible combinations. Tocheck if you have all combinations, raise 2 to the power equal to the number of input variables. This willgive you the total number of possible combinations. For example:EXAMPLE 1-AB = 2^{2} = 4 combinationsEXAMPLE 2-XYZ = 2^{3} = 8 combinationsX Y Z f0 0 0 00 0 1 00 1 0 00 1 1 01 0 0 01 0 1 01 1 0 01 1 1 1f = XYZAs with all AND gates, all the inputs must be HIGH at the same time to produce a HIGH output.Don’t be confused if the complement of a variable is used as an input. When a complement is indicated asan input to an AND gate, itmustalsobeHIGHtosatisfytheinputrequirementsofthegate. The Booleanexpression for the output is formulated based on the TRUE inputs that give a TRUE output. Here is anadage that might help you better understand the AND gate:In order to produce a 1 output, all the inputs must be 1. If any or all of the inputs is/are 0, then theoutput will be 0.Referring to the following examples should help you cement this concept in your mind. Remember,the inputs, whether the original variable or the complement must be high in order for the output to behigh. The three examples given are all AND gates with two inputs. Keep in mind the Boolean expressionfor the output is the result of all the inputs being HIGH.

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