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Enter Function Data
Choose the variable count, define labels, then supply minterms and optional don’t-care terms for exact minimization.
Example Data Table
This sample illustrates a four-variable function with don’t-cares and the reduced expressions returned by the minimizer.
| Variables | Minterms | Don’t-Cares | Reduced SOP | Reduced POS |
|---|---|---|---|---|
| 4 (A, B, C, D) | 0, 1, 2, 5, 6, 7, 8, 9, 10, 14 | 3, 11, 15 | A'D + B' + C | (B' + C + D) (A' + B' + C) |
Formula Used
1) Canonical Sum of Products
F = Σm(minterms)
Each listed minterm becomes a product term containing every variable. A binary 1 keeps the variable direct, while a binary 0 uses its complemented form.
2) Canonical Product of Sums
F = ΠM(maxterms)
Every zero-state becomes a sum clause. During clause building, a fixed 0 keeps the variable direct and a fixed 1 uses its complemented form.
3) Quine–McCluskey Combination Rule
0101 + 0111 → 01-1
Two terms combine when they differ in exactly one bit. The differing position becomes a dash, which removes one literal from the expression.
4) Selection Objective
The calculator identifies essential prime implicants first. It then picks the remaining cover that uses the fewest implicants and, if needed, the fewest literals.
How to Use This Calculator
Step 1
Select the number of input variables. The allowed decimal term range updates automatically from 0 up to 2n−1.
Step 2
Enter variable labels in order, such as A, B, C, D. The calculator fills missing labels automatically if fewer names are supplied.
Step 3
Type the function’s minterms as decimal indices. Separate values with commas or spaces and avoid repeating any term.
Step 4
Add optional don’t-care terms only when those states are irrelevant. They help reduce literal count but cannot overlap any minterm.
Step 5
Press the submit button. The minimized result appears above the form with canonical expressions, implicant tables, coverage details, and the full truth table.
Step 6
Use the export buttons to save a CSV summary or a PDF report for design reviews, coursework, or implementation notes.
Frequently Asked Questions
What does this calculator minimize?
It minimizes Boolean logic functions entered as minterms with optional don’t-cares. The page returns reduced SOP and POS forms, prime implicants, and a truth table.
Why are don’t-care terms useful?
Don’t-care states can be treated as either 0 or 1 during grouping. That flexibility often creates larger groups and lowers the final literal count.
How many variables can I enter?
This version supports two through six variables. That range keeps the output readable while still covering many coursework and digital design tasks.
Does the calculator show both SOP and POS forms?
Yes. It computes minimized SOP from ones and minimized POS from zero states. That helps you compare gate-level implementation choices quickly.
What happens if a minterm overlaps a don’t-care term?
The calculator blocks that input and shows a validation message. A state cannot be required as 1 and ignored at the same time.
Is the result exact or heuristic?
The page uses exact prime implicant generation and then selects a smallest remaining cover by implicant count and literal count for the supported size range.
Can I use custom variable names?
Yes. Enter labels such as X, Y, Z or Q1, Q2, Q3. Missing labels are filled automatically in sequence.
What is included in the CSV and PDF exports?
The exports include the selected inputs, reduced expressions, complexity metrics, and prime implicant tables from the current result panel.
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