Digital Electronics
Cheat sheet
Canonical Forms on One Card: Σm and ΠM
Can you write Σm(1,3,5,7) as a product of maxterms? Canonical forms on one card.
Quick check · tap an answer to continue
Lesson notes
Write a function as sum of minterms or product of maxterms from a truth table
Key points
- Minterm: An AND term with every variable once, true for exactly one input row.
- Minterm rule: 0 → A': For a minterm, complement any variable that is 0 in that row.
- Maxterm: An OR term with every variable once, false for exactly one input row.
- Maxterm rule: 0 → A: For a maxterm, keep a variable plain when it is 0, complement when 1.
- SOP = Σm(rows with 1): Sum of products lists the row indices where the output is one.
- POS = ΠM(rows with 0): Product of sums lists the leftover indices, so Σm(1,3,5,7) equals ΠM(0,2,4,6).
Takeaway: Σm lists the 1-rows, ΠM lists the 0-rows; together they cover all.
Quick check: In a maxterm, how is a variable written when its input value is 0?
- Complemented, like A'
- Uncomplemented, like A
- Left out of the term
A maxterm must be false on its row, so a 0 input appears as the plain variable.
mintermmaxtermSOPPOS
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