# Physics

Daytona State College

Department of Engineering Technology CET 3198 Digital Systems – Fall 2013

Homework 1 Due Date: September 29th 11:59 p.m.

Submit the homework via drop-box. For each one of the questions justify your answer and show your work.

1. Find the minimum cost implementation in SOP (Sum of Products) and POS (Product of Sums)for the function f(x1,x2,x3)  =  Σ  m(1,2,3,5).  Using  the  formula  for  determining  the  cost  of  an   implementation, calculate the cost.

2. A four variable logic function that is equal to 1 if any three or all four of its variables are equal to 1 is called majority function. Design a minimum cost SOP circuit that implements this majority function.

3. Find the minimal SOP expression for f(x1,x2,x3, x4)  =  Σ  m(1,5,7,9,11,15)   4. Find the minimum sum-of-product of the following functions:

a. F=X’Z  +  XY  +  XY’Z   b. F=A’C’D  +  B’CD  +  AC’D+BCD   c. F=WXZ’  +  WX’YZ  +  XZ   d. F=ABC’D’  +A’BC’+ABD+A’CD+BCD’

5. A circuit with two outputs has to implement the following functions: f(x1,..,x4)  =  Σ  m(0,2,4,6,7,9)  + D(10,11) g(x1,..,x4)=  Σ  m(2,4,9,10,15)+D(0,13,14)

Design the minimum-cost circuit and compare its cost with combined costs of two circuits that implements f and g separately. Assume that the input variables are available in both complemented and uncomplemented forms.

NOTE: Calculate the cost of a logic circuit as the number of gates plus the total number of inputs to all gates in the circuit. Assuming that inputs are available both true and complemented form at zero cost. If an inversion is needed inside a circuit, then the corresponding NOT gate and its input are included in the cost. (See chapter 4 in the book)

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