Karnaugh map (K-map)
What is a K-map?
A Karnaugh map (K-map) is a visual method used to simplify the algebraic expressions in Boolean functions without having to resort to complex theorems or equation manipulations. A K-map can be thought of as a special version of a truth table that makes it easier to map out parameter values and arrive at a simplified Boolean expression.
What is SOP?
What is POS?
2-variable K-map sample
3-variable K-map sample
4-variable K-map sample
SOP
| ab/cd | 00 | 01 | 11 | 10 | |
|---|---|---|---|---|---|
| c'd' | c'd | cd | cd' | ||
| 00 | a'b' | 0 | 1 | 3 | 2 |
| 01 | a'b | 4 | 5 | 7 | 6 |
| 11 | ab | 12 | 13 | 15 | 14 |
| 10 | ab' | 8 | 9 | 11 | 10 |
POS
| a/bc | 00 | 01 | 11 | 10 | |
|---|---|---|---|---|---|
| c+d | c+d' | c'+d' | c'+d | ||
| 00 | a+b | 0 | 1 | 3 | 2 |
| 01 | a+b' | 4 | 5 | 7 | 6 |
| 11 | a'+b' | 12 | 13 | 15 | 14 |
| 10 | a'+b | 8 | 9 | 11 | 10 |
Truth table of min term and max term (2 variable)
| a | b | SOP (Min Term) | POS (Max Term) |
| 0 | 0 | a'b' (m0) | a+b (M0) |
| 0 | 1 | a'b (m1) | a+b' (M1) |
| 1 | 0 | ab' (m2) | a'+b (M2) |
| 1 | 1 | ab (m3) | a'+b' (M3) |
Truth table of min term and max term (3 variable)
| a | b | c | SOP (Min Term) | POS (Max Term) |
| 0 | 0 | 0 | a'b'c' (m0) | a+b+c (M0) |
| 0 | 0 | 1 | a'b'c (m1) | a+b+c' (M1) |
| 0 | 1 | 0 | a'bc' (m2) | a+b'+c (M2) |
| 0 | 1 | 1 | a'bc (m3) | a+b'+c' (M3) |
| 1 | 0 | 0 | ab'c' (m4) | a'+b+c (M4) |
| 1 | 0 | 1 | ab'c (m5) | a'+b+c' (M5) |
| 1 | 1 | 0 | abc' (m6) | a'+b'+c (M6) |
| 1 | 1 | 1 | abc (m7) | a'+b'+c' (M7) |
Truth table of min term and max term (4 variable)
| a | b | c | d | SOP (Min Term) | POS (Max Term) |
| 0 | 0 | 0 | 0 | a'b'c'd' (m0) | a+b+c+d (M0) |
| 0 | 0 | 0 | 1 | a'b'c'd (m1) | a+b+c+d' (M1) |
| 0 | 0 | 1 | 0 | a'b'cd' (m2) | a+b+c'+d (M2) |
| 0 | 0 | 1 | 1 | a'b'cd (m3) | a+b+c'+d' (M3) |
| 0 | 1 | 0 | 0 | a'bc'd' (m4) | a+b'+c+d (M4) |
| 0 | 1 | 0 | 1 | a'bc'd (m5) | a+b'+c+d' (M5) |
| 0 | 1 | 1 | 0 | a'bcd' (m6) | a+b'+c'+d (M6) |
| 0 | 1 | 1 | 1 | a'bcd (m7) | a+b'+c'+d' (M7) |
| 1 | 0 | 0 | 0 | ab'c'd' (m8) | a'+b+c+d (M8) |
| 1 | 0 | 0 | 1 | ab'c'd (m9) | a'+b+c+d' (M9) |
| 1 | 0 | 1 | 0 | ab'cd' (m10) | a'+b+c'+d (M10) |
| 1 | 0 | 1 | 1 | ab'cd (m11) | a'+b+c'+d' (M11) |
| 1 | 1 | 0 | 0 | abc'd' (m12) | a'+b'+c+d (M12) |
| 1 | 1 | 0 | 1 | abc'd (m13) | a'+b'+c+d' (M13) |
| 1 | 1 | 1 | 0 | abcd' (m14) | a'+b'+c'+d (M14) |
| 1 | 1 | 1 | 1 | abcd (m15) | a'+b'+c'+d' (M15) |
Possible pairs and quads (4 variable)
