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Minimize the following expression using k-Map Y = ∑m (0,1,5,9,13,14,15) + d (3,4,7,10,11)?
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Minimize the following expression using k-Map Y = ∑m (0,1,5,9,13,14,15...
Understanding the Expression
The expression given is Y = ∑m (0,1,5,9,13,14,15) + d (3,4,7,10,11). Here, 'm' represents the minterms that contribute to the function Y, and 'd' represents the don't-care conditions.
Constructing the K-Map
1. K-Map Layout: For a 4-variable K-map (A, B, C, D), the cells are arranged as follows:
AB\CD | 00 | 01 | 11 | 10
--------------------------
00 | 0 | 1 | 3 | 2
01 | 4 | 5 | 7 | 6
11 | 12 | 13 | 15 | 14
10 | 8 | 9 | 11 | 10
2. Filling the K-Map:
- Place 1s for minterms: 0, 1, 5, 9, 13, 14, 15.
- Place Xs for don't-care conditions: 3, 4, 7, 10, 11.
AB\CD | 00 | 01 | 11 | 10
--------------------------
00 | 1 | 1 | X | 0
01 | X | 1 | X | X
11 | 0 | 1 | 1 | 1
10 | 0 | 1 | X | X
Grouping 1s and Xs
- Group 1: (0,1) - Horizontal pair.
- Group 2: (5,13,14,15) - 4-cell rectangle.
- Group 3: (9, 13, 15) - Vertical pair.
Deriving the Simplified Expression
After grouping:
1. Group 1: A'B'
2. Group 2: BC
3. Group 3: ACD
Thus, the minimized expression is:
Y = A'B' + BC + ACD
This expression represents the minimized form of the original function using the K-map.
The expression given is Y = ∑m (0,1,5,9,13,14,15) + d (3,4,7,10,11). Here, 'm' represents the minterms that contribute to the function Y, and 'd' represents the don't-care conditions.
Constructing the K-Map
1. K-Map Layout: For a 4-variable K-map (A, B, C, D), the cells are arranged as follows:
AB\CD | 00 | 01 | 11 | 10
--------------------------
00 | 0 | 1 | 3 | 2
01 | 4 | 5 | 7 | 6
11 | 12 | 13 | 15 | 14
10 | 8 | 9 | 11 | 10
2. Filling the K-Map:
- Place 1s for minterms: 0, 1, 5, 9, 13, 14, 15.
- Place Xs for don't-care conditions: 3, 4, 7, 10, 11.
AB\CD | 00 | 01 | 11 | 10
--------------------------
00 | 1 | 1 | X | 0
01 | X | 1 | X | X
11 | 0 | 1 | 1 | 1
10 | 0 | 1 | X | X
Grouping 1s and Xs
- Group 1: (0,1) - Horizontal pair.
- Group 2: (5,13,14,15) - 4-cell rectangle.
- Group 3: (9, 13, 15) - Vertical pair.
Deriving the Simplified Expression
After grouping:
1. Group 1: A'B'
2. Group 2: BC
3. Group 3: ACD
Thus, the minimized expression is:
Y = A'B' + BC + ACD
This expression represents the minimized form of the original function using the K-map.
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Minimize the following expression using k-Map Y = ∑m (0,1,5,9,13,14,15) + d (3,4,7,10,11)?
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Minimize the following expression using k-Map Y = ∑m (0,1,5,9,13,14,15) + d (3,4,7,10,11)? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Minimize the following expression using k-Map Y = ∑m (0,1,5,9,13,14,15) + d (3,4,7,10,11)? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Minimize the following expression using k-Map Y = ∑m (0,1,5,9,13,14,15) + d (3,4,7,10,11)?.
Minimize the following expression using k-Map Y = ∑m (0,1,5,9,13,14,15) + d (3,4,7,10,11)? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Minimize the following expression using k-Map Y = ∑m (0,1,5,9,13,14,15) + d (3,4,7,10,11)? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Minimize the following expression using k-Map Y = ∑m (0,1,5,9,13,14,15) + d (3,4,7,10,11)?.
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