Q7: Minimization

Time Estimate15-30 minutes   Grade Impact0.5%   DueSep 21 @ 12pm  

Objective
Reinforce an understanding of PoS and SoP.

Additional Materials & Formats
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Free Response Questions

1. What is the purpose of minimization?

2. Why are prime implicants useful in a practical circuit design setting?

3. Explain the difference between a variable and a literal.

Multiple Choice Questions

4. In a 4-variable K-map (16 cells), the largest allowed grouping size is

   • 4
   • 8
   • 16
   • 32
   • Trick question – it’s infinite

5. Grouping two adjacent 1s in a K-map reduces the number of variables in the corresponding product term by

   • 0
   • 1
   • 2
   • 3

6. Don’t-care conditions in a K-map may be used to

   • force a function to zero
   • be treated as either 0 or 1 to enable larger groups
   • replace 0 or 1 values in the design specification
   • convert minterms to maxterms

7. Which grouping is NOT allowed in a 4-variable Karnaugh map?

   • A wrap-around group across the left and right edges
   • A group of 4 cells that form a square
   • A group of 6 cells arranged in a 2x3 configuration
   • A group of 8 cells spanning two rows

8. A prime implicant that covers a minterm not covered by any other implicant is called

   • redundant implicant
   • essential prime implicant
   • combined implicant
   • sub-implicant

9. Gray code ordering in K-map labeling ensures that any two adjacent cells differ by

   • exactly 1 bit
   • exactly 2 bits
   • at most 2 bits
   • not applicable – it depends on the K-map

10. When minimizing to a Product of Sums (PoS) form using a K-map, you should group

    • the 1s
    • the 0s
    • only the don’t-cares
    • neither 0s nor 1s