Question

1. Using truth tables, determine whether the following expressions are the same or not. Do not simplify equations.
   1. a'b + a'c + ac
   2. b(a'c' + c) + b'c
   3. c + a'b'

2. Simplify the following expressions using algebraic rules:
   1. (a+b+c)(a’+b+c)(a+b’+c’)(a’+b’+c’) (2 terms, 4 literals – POS form)

The rest will be SOP form:

2. ab'c + bd + bcd'+ ab'c' + abc'd (3 terms, 6 literals)
3. xyz’ + x’yz’ + x’yz + xyz (1 terms, 1 literal)
4. a’b’c’ + a’bc’ + a’bc + ab’c + abc’ + abc (3 terms, 5 literals)

3. Find the complement of the following expression. Then, simplify the complement as much as you can.  (Only single variables may be complemented in your answer --- (a+b)’ is not acceptable part of answer format).

(a + b)(b’ + c) + d’(a’b + c)

4. Consider the following function with don’t cares:

g(x,y,z)=åm(5,6)+åd(1,2,4)

      Determine if any of the following expressions can be used as a solution for g? Explain your answers.

            

1. z' + xy'z
2. x(y' + z')
3. yz' + y'z

5. Draw the diagram of the following expressions using only NAND gates. Assume all inputs are available both uncomplemented and complemented.

Do not simplify equations.

1. F=a’bd’+c’d+bcd
2. G=z(y’+x’w’) + w’(xy’+zx’)

Answer 1

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