Given the following Karnaugh map, which one of the following represents the…
2001
Given the following Karnaugh map, which one of the following represents the minimal Sum-Of-Products of the map?
| wx | w’x’ | w’x | wx | wx’ |
yz |
| 00 | 01 | 11 | 10 |
y’z’ | 00 | 0 | D | 0 | D |
y’z | 01 | D | 1 | D | 1 |
yz | 11 | 0 | D | 1 | 0 |
yz’ | 10 | 0 | 1 | D | 0 |
- A.
xy + y’z
- B.
wx’y’ + xy + xz
- C.
w’x + y’z + xy
- D.
xz + y
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Correct answer: A
1. Analyze the K-Map and Identify Groups We need to cover all the '1's in the Karnaugh map using the largest possible groups (grouping 1s and Don't Cares 'D').
Group 1 (Row 1):
There are 1s at indices 0101 (m5) and 1001 (m9).
We can form a Quad (group of 4) using the entire second row (y′z) which contains: D, 1, D, 1.
Cells: 0001,0101,1101,1001.
Common Literal: This row corresponds to y′z.
Group 2 (Bottom-Right Block):
There are 1s at indices 0110 (m6) and 1111 (m15).
We can form a Quad using cells 0110,0111,1111,1110 (Indices 6, 7, 15, 14).
Note: Cell 7 and 14 are 'D'.
Logic:
Columns involved: w′x (01) and wx (11) → x is 1.
Rows involved: yz (11) and yz′ (10) → y is 1.
Common Literal: xy.
2. Verify Coverage
y′z covers minterms 5 and 9.
xy covers minterms 6 and 15.
All 1s (5, 6, 9, 15) are covered.
3. Conclusion The minimal Sum-Of-Products (SOP) expression is the sum of these groups.
Expression: xy+y′z
Correct Option: (A)
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