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Question 3. Combinational Logic implementation (6 marks)
A, B, C and D are four binary input signals. Lets define the function F(A, B, C, D) such that F=1 if and only if there are more ones among the inputs than zeros.
a) Write down the truth table of F(A, B, C, D). (1 mark)
b) Express F as a function of minterms in the form F=m(???). (0.5 marks)
c) Simplify F into a SOP function and implement it using AND/OR circuit.
(Note: for your implementation you can either use K-map or boolean algebra
theorems and axioms). (0.5 marks)
d) Use DeMorgan Theorem in order to implement F using NAND-NAND
implementation. Write down the boolean expression and draw the schematic.
(0.5 marks)
e) Compare the implementation complexities of c) and d) in terms of equivalent
gates in CMOS technology:
How many equivalent gates do implementations c) and (d) require? (1mark)
f) Express F as a function of maxterms in the form F=M(???). (0.5 marks)
g) Simplify F into a POS function and implement it using OR/AND circuit.
(0.5 marks)
h) Use DeMorgan Theorem in order to translate F into a NOR/NOR
implementation. Write down the boolean expression and draw the schematic.
(0.5 marks)
i) Compare the implementation complexities of g) and h) in terms of equivalent
gates in CMOS technology:
How many equivalent gates do implementations g) and (h) require? (1mark)

Mid-term Exam#1. Spring 2004, 3