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Minimize the logic function using Quine-Mc-clusky method.$\\ \;$ $F(A B C D)=\sum m (1,3,7,9,10,11,13,15)$
written 9.5 years ago by gravatar for teamques10 teamques10 ★ 70k •   modified 9.5 years ago

Mumbai University > COMPS > Sem 3 > Digital Logic Design and Analysis

Marks: 10 M

Year: May 2015
digital logic design
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written 9.5 years ago by gravatar for teamques10 teamques10 ★ 70k •   modified 9.5 years ago

Step 1: List all minterm in the binary form

Minterm Binary Representation
$M_1$ 0 0 0 1
$M_3$ 0 0 1 1
$M_7$ 0 1 1 1
$M_9$ 1 0 0 1
$M_{10}$ 1 0 1 0
$M_{11}$ 1 0 1 1
$M_{13}$ 1 1 0 1
$M_{15}$ 1 1 1 1
Minterms Binary Representation
$M_1$ $0 0 0 1$
$M_3 \\ M_9 \\ M_{10}$ $0 0 1 1 \\ 1 0 0 1 \\ 1 0 1 0$
$M_7 \\ M_{11} \\ M_{13}$ $0 1 1 1 \\ 1 0 1 1 \\ 1 1 0 1$
$M_{15}$ $1 1 1 1$

Step 2 : Arrange Minterms according to categories of 1’s.

$\\ \;$

Step 3: Comparing each binary number with every term in higher category and if they differ by one position put a check mark and copy the term in the next column with ‘_’ in that position.

Minterm Binary Representation
1,3 0 0 0_1 √
1,3 0 0 0_1√
3,3 _ 0 0 1 √
3,7 0 _ 1 1 √
3,11 _ 0 1 1 √
9,11 1 0 _ 1 √
9,13 1 _ 0 1 √
10,11 1 0 1 _
7,15 _ 1 1 1 √
11,15 1 _ 1 1 √
13,15 1 1 _ 1 √

Step 4 : Report procedure until a single pass through cycle yields no further elimination.

Minterm Binary Representation
1,3,9,11 _ 0 _ 1
3,7,11,15 _ _ 1 1
9,11,13,15 1 _ _ 1

Step 5 : List Prime Implication.

Prime Implication Binary Representation
$A\overline{B}C$ 1 0 1 _
$\overline{B}D$ _ 0 _ 1
C D _ _ 1 1
A D 1 _ _ 1

Step 6 : Select the Minimum number of prime Implication which must cover all the minterms.

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$Y=A\overline{B}C+\overline{B}D+CD+AD$

Final Expression is Y=(1 0 1 _ )+(_ 0 _ 1)+(_ _ 1 1)+(1 _ _ 1)
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