Question

Given the sum-of-minterms expression F = m4 + m6 + m7 + m12 + m14 + m15

a. Using letters, A-D for the bits, what sum of minterms does this expression represent?

b. Plot the following in a Karnaugh Map.

c. Using the karnaugh map, state the simplest sum-of-products expression.

d. Using the karnaugh map, state the simplest product-of-sums expression.

e. Demonstrate how you would use a 4-line to 16 line demultiplexer to implement the circuit. You may use either the answer to part a or part c to implement the circuit. If you use part c, then you only need a 3-line to 8 line demultiplexer. Test your new circuit with logisim

Answer 1

According to the question the given sum-of-minterms expression F=m4+m6+m7+m12+m14+m15

(a.) Using letters A-D for the bits, the sum of minterms for the above expression represent is as follows:-

F = m4+m6+m7+m12+m14+m15

=> F = Sigma(4,6,7,12,14,15)

(b.) The Karnough map for the above expression is as follows:-

(c.) Using Karnough map we minimized the above expression, this can be done by grouping the minterms in the size of power of 2, first we try to form the largest group possible, if it is not achieved then we try to form the lower groups, In this manner we form the group and get the minimized expression as follows:-

here minterm 6,7 14,15 form a quad group and minterms 4,6,12,14 form an other quad group , therefore the minimized expression of SOP form is as follows:-

F = BC + BD'

(d.) Using K map the simplest POS form can be determine by putting 0's in all the blank spaces of the kmap

Now we form the group, the grouping can be done in same manner as it was in the SOP form but now we form the group of 0's ,the expression can be determine in same manner but in opposite way that is while writing 0 refers to non-compliment variable and vice-versa,

Using this rule the POS form of the expression will be as follows:-

here maxterm 0,1,2,3,8,9,10,11 form a octate group and maxterms 1,5,9,13 form a quad group , therefore the minimized expression of POS form is as follows:-

F = B.(C+D')