write down the truth table of three variables A,B,C
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Answer:
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Explanation:
The table used to represent the boolean expression of a logic gate function is commonly called a Truth Table. A logic gate truth table shows each possible input combination to the gate or circuit with the resultant output depending upon the combination of these input(s).
For example, consider a single 2-input logic circuit with input variables labelled as A and B. There are “four” possible input combinations or 22 of “OFF” and “ON” for the two inputs. However, when dealing with Boolean expressions and especially logic gate truth tables, we do not general use “ON” or “OFF” but instead give them bit values which represent a logic level “1” or a logic level “0” respectively.
Then the four possible combinations of A and B for a 2-input logic gate is given as:
Input Combination 1. – “OFF” – “OFF” or ( 0, 0 )
Input Combination 2. – “OFF” – “ON” or ( 0, 1 )
Input Combination 3. – “ON” – “OFF” or ( 1, 0 )
Input Combination 4. – “ON” – “ON” or ( 1, 1 )
Therefore, a 3-input logic circuit would have 8 possible input combinations or 23 and a 4-input logic circuit would have 16 or 24, and so on as the number of inputs increases. Then a logic circuit with “n” number of inputs would have 2n possible input combinations of both “OFF” and “ON”.
So in order to keep things simple to understand, in this tutorial we will only deal with standard 2-input type logic gates, but the principals are still the same for gates with more than two inputs.
Then the Truth tables for a 2-input AND Gate, a 2-input OR Gate and a single input NOT Gate are given as:
2-input AND Gate
For a 2-input AND gate, the output Q is true if BOTH input A “AND” input B are both true, giving the Boolean Expression of: ( Q = A and B ).
Explanation:
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