In Karnaugh Maps, which of the following terms refers to a group of adjacent…
2025
In Karnaugh Maps, which of the following terms refers to a group of adjacent cells that can be combined to simplify a logic expression?
- A.
Block
- B.
Cluster
- C.
Pair
- D.
Group
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Correct answer: D
Important Terms Used in Karnaugh Map (K-Map)
1. Karnaugh Map (K-Map)
A graphical method used to simplify Boolean expressions and reduce logic gates in digital circuits.
2. Cell
Each box in a K-Map is called a cell.
Every cell represents one minterm or maxterm.
3. Adjacent Cells
Cells differing by only one variable are called adjacent cells.
4. Group / Grouping
Combining adjacent cells together for simplification is called grouping.
5. Pair
A group containing 2 adjacent cells.
6. Quad
A group containing 4 adjacent cells.
7. Octet
A group containing 8 adjacent cells.
8. Singleton
A group containing only one cell.
Boolean Expression Terms
9. Minterm
A product term in which all variables appear once in either complemented or uncomplemented form.
Represented by: Σm
Example:
A'BC
10. Maxterm
A sum term in which all variables appear once.
Represented by: ΠM
Example:
A + B' + C
11. SOP (Sum of Products)
ORing of multiple product terms.
Example:
AB + A'C
12. POS (Product of Sums)
ANDing of multiple sum terms.
Example:
(A+B)(A'+C)
13. Boolean Expression
Logical expression formed using AND, OR, and NOT operations.
14. Variable
Input symbols used in Boolean expressions such as A, B, C, D.
Grouping Related Terms
15. Implicant
A term that covers one or more cells containing 1s in a K-Map.
Example:
A group formed from adjacent 1s.
16. Prime Implicant
The largest possible valid group formed in K-Map that cannot be combined further.
Example:
Quad is preferred over Pair
Octet is preferred over Quad
17. Essential Prime Implicant
A prime implicant that covers at least one unique cell not covered by any other group.
Meaning:
Without this group, that cell cannot be included in the final simplified expression.
18. Redundant Prime Implicant
A prime implicant that is not necessary because all its cells are already covered by other groups.
19. Covered Cell
A cell included inside a group.
20. Uncovered Cell
A cell not included in any group.
21. Overlapping Group
When one cell belongs to more than one group.
22. Dominant Group
The largest possible group preferred during simplification.
Special K-Map Terms
23. Don’t Care Condition
Input combinations whose output does not matter.
Represented by:
X
These may be treated as either 0 or 1 for simplification.
24. Gray Code
Special binary sequence used in K-Map arrangement where only one bit changes at a time.
Example:
00, 01, 11, 10
25. Wrapping Around
In K-Map, edge cells are also considered adjacent.
26. Power-of-2 Grouping
Groups must contain cells in powers of 2:
1, 2, 4, 8, 16 …
27. Simplification
Process of reducing Boolean expressions using grouping techniques.
28. Logic 1 Cell
Cell containing binary value 1 used for SOP simplification.
29. Logic 0 Cell
Cell containing binary value 0 used for POS simplification.
Canonical Forms
30. Canonical SOP
Expression written completely in minterm form.
31. Canonical POS
Expression written completely in maxterm form.