Question

#9) You are to implement the following function F(A,B,C,D,E,F) which outputs a 1 whenever the binary number represented by ABCDE is ODD and 0 otherwise. A is the MSB and E is the LSB.

Draw the function F(A,B,C,D,E,F) and show the work that led you to that answer.

Since I am not so sadistic as to have you draw the truth table of a 6 variable function and draw the K-map of such a function, you should realize, as a HINT, that your circuit is the simplest possible one and your explanation should be 1 sentence AT THE MOST !  

Answer 1

The simplest function that satisfy the given condition is F=E.

Explanation:

The binary number which is represented by ABCDE with A as MSB and E as LSB can be ODD only when the E is 1 and then the output is 1 for E is ODD as per given question.

For example,let the ABCDE be 10011.It's value is 19,an ODD number because E is 1

If the E is 0, then the binary number becomes even.Then the output becomes 0.

For example,let the ABCDE be 10010,it's value is 18, an EVEN number because E is 0

In both the cases,the output of the function is equal to the value of E.