K-Map Solver
A K-map groups adjacent 1s into the largest power-of-two blocks: Σm(0, 1, 2, 5, 6, 7, 8, 9, 10, 14) simplifies to F(A, B, C, D) = B′C′ + CD′ + A′BD.
Separate with spaces or commas; leave blank if none.
F(A, B, C, D) = B′C′ + CD′ + A′BD
- Minimal POS
- F = (B + C′ + D′)(B′ + C + D)(A′ + B′ + D′)
- Prime implicants
- A′C′D, A′BD, A′BC, B′C′, B′D′, CD′
- Essential prime implicants
- B′C′, CD′
- Terms in minimal SOP
- 3
- Literals in minimal SOP
- 7
Step-by-step solution
- Group minterms (and don’t-cares) that differ in one bit, repeatedly (Quine–McCluskey = K-map grouping)
- Keep essential prime implicants, then the fewest others that cover the rest
- F = B′C′ + CD′ + A′BD
K-Map Solver Formula
F = Σm(…) + d(…) → minimal SOP / POS
Quine–McCluskey with an exact minimum cover
Worked Example
F(A, B, C, D) = Σm(0, 1, 2, 5, 6, 7, 8, 9, 10, 14):
- Group minterms (and don’t-cares) that differ in one bit, repeatedly (Quine–McCluskey = K-map grouping)
- Keep essential prime implicants, then the fewest others that cover the rest
- F = B′C′ + CD′ + A′BD
Prime implicants: A′C′D, A′BD, A′BC, B′C′, B′D′, CD′ · Essential prime implicants: B′C′, CD′ · Terms in minimal SOP: 3 · Literals in minimal SOP: 7
GATE tip
GATE often asks how many essential prime implicants a function has, or how many literals the minimal form needs; both are shown above. A function can have more than one minimal form.
More Digital Logic and Number Representation Calculators
-
Number Base Converter
N = Σ dᵢ·bⁱ
integer part: repeated division; fraction: repeated multiplication by the base
Example: The decimal number 45.625: Binary = 101101.101.
-
Two’s Complement Calculator
−x = invert(x) + 1
n-bit range −2ⁿ⁻¹ … 2ⁿ⁻¹ − 1
Example: −45 as an 8-bit number: 8-bit two’s complement = 1101 0011.
-
IEEE 754 Floating Point Converter
value = (−1)ˢ × 1.m × 2^(e − bias)
single: 8-bit exponent, bias 127, 23-bit mantissa; double: 11, 1023, 52
Example: −12.375 in single precision: IEEE 754 single (hex) = 0xC1460000.
Frequently asked questions
What is an essential prime implicant?
A prime implicant that is the only one covering some minterm, so it must appear in every minimal expression.
How do don’t-care conditions help?
They can be treated as 1 or 0, whichever gives larger groups, and so fewer literals.
Sources
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). K-Map Solver. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/k-map-solver/
IEEE
Scientific Converters, "K-Map Solver," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/k-map-solver/