Consider the BCD-to-Seven-Segment Decoder

I.          (20 points) Consider the BCD-to-Seven-Segment Decoder design as discussed in the textbook (pages 30-31). Use K-maps to obtain a minimum SOP form for the output functions corresponding to Segment d and Segment g. Remember to exploit Don’t Care minterms 10 to 15. Label the K-maps exactly as shown in the book: X3 X2 for rows and X1 X0 for columns.

II.         (30 points) Consider the following Boolean functions:

 

              F1( A, B, C) = A . B  + A’ . B. C ‘ 

 

              F2( A, B, C ) = B . C ‘  + A. B’ . C + A . B

 

(i)                
Implement F1 and F2 using one 3:8 Decoder module and two OR gates.

 

(ii)              
Implement F1 and F2 using two 4:1 Multiplexers and one optional NOT gate.

 

(iii)            
Implement F1 and F2 using a PLA that has 3 inputs, 2 outputs, and 4 products. Show the PLA logic using the notation as per Figure 1.35, page 44 of your text.