Truth tables for functions with large number of inputs will have lots of rows. It’s sometimes possible to keep truth tables more compact (and hence easier to read and understand) if we allow the use of “don’t cares” when specifying an input value. A “don’t care”, written as “—“ or “X” in the appropriate input column, indicates that the value of the output doesn’t depend on that input given the specified values for the other inputs. For example, here are two equivalent truth tables for the 2-input Boolean OR function: if either input (A,B) is “1”, the output (Z) is “1”; otherwise the output is 0.A B | Z======|=== ======|===0 0 | 01 – | 1- 1 | 11 1 | 1Note that one has to be careful when building truth tables with don’t cares: the truth table must still specify only one possible output value for any particular combination of inputs.Consider the truth table for a 7-input priority encoder which examines its seven inputs (I1, I2, I3, I4, I5, I6, I7) and outputs a 3-bit binary number indicating the highest-priority input which has a value of “1”, where I7 has the highest priority and I1 the lowest. If no inputs are “1”, the encoder outputs “000”. If I7 is “1”, the encoder outputs “111”. If I7 is “0” and I6 is “1”, the encoder outputs “110”. And so on…Normally the truth table for a 7-input logic function would have 128 rows. Give a much smaller truth table for the encoder using “don’t cares”.
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