ECE 102 - Homework 4

Due  09/19/2017

1. Write the function X given by the following truth table as a canonical SOP, a minimum SOP, a canonical POS and a minimum POS.
       
   P  Q  R    X
   0  0  0    1
   0  0  1    0
   0  1  0    1
   0  1  1    0
   1  0  0    0
   1  0  1    1
   1  1  0    0
   1  1  1    1
   
   
2. A flow rate sensing device used on a liquid transport pipeline functions as follows. The device provides a 5-bit output (A,B,C,D,E) where all five bits are zero if the flow rate is less than 10 gallons per minute. The first bit is 1 if the flow rate is at least 10 gal/min; the first and second bits are 1 if the rate is at least 20 gal/min; first, second and third bits are 1 if the rate is at least 30 gal/min; and so on. A display device uses (A,..E) as inputs and provides two outputs Y,Z. Y is 1 iff the flow rate is less than 30 gal/min, and Z =1 iff the flow rate is at least 20 gal/min but less than 50 gal/min. Write equations for Y and Z. Design a circuit to produce Y, Z  from (A,...E).
   
   
3. Consider a circuit with three data inputs D2, D1, D0, a control input C, and two outputs R1,R0, which implements the following function:
   When C = 0,  the outputs R1,R0 contain the binary representation of number of 0’s in the data inputs.
   When C = 1, R1, R0 contain the binary representation of number of 1’s in the data inputs.
   Ex. If C=0, D2=1,D1=0,D0=1, then R1=0, R0=1
       If C=1, D2=1,D1=0,D0=1, then R1=1, R0=0
   Design a circuit to implement this function using AND-OR circuits.
   
   
4. Enter F(A,B,C,D) = (A+D')'(BC'+B'C) in a truth table, and
   (a) express F as a canonical SOP
   (b) express F as a canonical POS