3-Variable K-Map Solution (Step-by-Step, in 2 parts)

"Part 1 — Problem Setup"

Given,

• Minterms: \( \Sigma m(1,2,4,5,7) \)
• Don’t cares: (none)
• Variables: \(a, b, c\)
• Method: Karnaugh Map (K-map)

K-map layout (Gray code on columns \(bc\): 00, 01, 11, 10)

Cell–minterm mapping (row \(a=0\): m0, m1, m3, m2; row \(a=1\): m4, m5, m7, m6).

Part 2 — Grouping & Simplification:

Group-1: 2-cell grouping \((5,7)\)
Cells: row \(a=1\), cols \(bc=01,11\) → \(b\) changes, \(a=1\), \(c=1\)

• Term: ac

Group-2: 2-cell grouping \((4,5)\)
Cells: row \(a=1\), cols \(bc=00,01\) → \(c\) changes, \(a=1\), \(b=0\)

• Term: ab'

Group-3: 2-cell grouping \((1,5)\)
Cells: col \(bc=01\), rows \(a=0,1\) → \(a\) changes, \(b=0\), \(c=1\)

• Term: b'c

Group-4: 1-cell grouping \((2)\)
Cell: \(m_2\) at \(a=0,b=1,c=0\)

• Term: a'bc'

Final minimized SOP:

F(a,b,c) = ac + ab' + b'c + a'bc'

Coverage check (by minterm):

• \(m_5, m_7 \rightarrow ac\)
• \(m_4, m_5 \rightarrow ab'\)
• \(m_1, m_5 \rightarrow b'c\)
• \(m_2 \rightarrow a'bc'\)

DLD Lab 4.2 (Circuit Design with K-Map solution )

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TinkerCad এর জন্যঃ

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এর আগের গুলোতে আমরা SOP বের করেছিলাম, এবারে আমাদের POS বের করে সেগুলো KMap দিয়ে minmize করে পরবর্তীতে সেগুলোকে TinkerCad এ circuit তৈরী করতে হবেঃ

LAB - 4.3:

Maxterms: ΠM(1, 2, 4, 5, 7)

LAB - 4.4 :

Maxterms: ΠM(2,3,6,7,8,10,13,15)

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Solution will be upated soon.