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10. Develop a logic circuit called "Simple Multiples." This circuit accepts 4 bits that represent a BCD number. It has three outputs:

• A HIGH on output X indicates that the number is a multiple of 2
• A HIGH on output Y indicates that the number is a multiple of 3
• A HIGH on output Z indicates that the number is a multiple of both 2 and 3 *0 counts as a multiple for all of these

Create a truth table for this circuit

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Answer:

Explanation:

"Simple Multiples Logic Circuit Development"

From the attached file below;

The first diagram illustrate the truth table. The input consist of binary coded decimal with  its 16  possible output. As stated in the input, assuming we have 0010 which the value is 2, thus ; it is said to be divisible by 2 , then we enter the output of x  to be 1 and the remaining as zeros

The second diagram talks about the output x; the representation of x is 1 there and it was added up. The use case employed is  [tex]x + \bar {x} =1[/tex] which in turn yield output [tex]\bar {A3}[/tex]

The second to the last diagram represents output Y and Z.

As output Y can be further disintegrated ; we insert XNOR gate for the expressions. The expression is  [tex]a.b+(\bar{a}. \bar{b})[/tex]

The last diagram is the logic diagram.

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