In the following examples the distinguished 1-cells are marked in the upper left corner of the cell with an asterisk (*). The essential prime implicants are circled in blue, the prime implicants are circled in black, and the non-essential prime implicants included in the minimal sum are shown in red.
Example 1
- Prime Implicants: 5
- Distinguished 1-Cells: 2
- Essential Prime Implicants: 2
- Minimal Sums: 1
Y = A'CD' + AC'D + BCD
Example 2
- Prime Implicants: 7
- Distinguished 1-Cells: 2
- Essential Prime Implicants: 2
- Minimal Sums: 1
Y = B'D' + AD' + A'C'D + BCD
Example 3
- Prime Implicants: 6
- Distinguished 1-Cells: 2
- Essential Prime Implicants: 2
- Minimal Sums: 3
Y = AB'C' + A'CD' + AC'D + BCD
Y = AB'C' + A'CD' + ABD + A'BC
Y = AB'C' + A'CD' + ABD + BCD
Example 4
- Prime Implicants: 5
- Distinguished 1-Cells: 3
- Essential Prime Implicants: 3
- Minimal Sums: 1
- Y = A'B' + A'C' + ABC + A'D
Example 5
- Prime Implicants: 4
- Distinguished 1-Cells: 4
- Essential Prime Implicants: 4
- Minimal Sums: 1
Y = A'C + A'B + BD + CD
Example 6
- Prime Implicants: 5
- Distinguished 1-Cells: 3
- Essential Prime Implicants: 3
- Minimal Sums: 1
- Y = B'D + BC' + AB
Example 7
- Prime Implicants: 8
- Distinguished 1-Cells: 0
- Essential Prime Implicants: 0
- Minimal Sums: 2
Y = A'B'C + A'BD + ABC' + AB'D'
Y = B'CD' + A'CD + BC'D + AC'D'
Example 8
- Prime Implicants: 3
- Distinguished 1-Cells: 8
- Essential Prime Implicants: 3
- Minimal Sums: 1
Y = B'C + D + BC'
5-Variable Karnaugh Maps
For these you must circle the prime implicants on each map individually and then the prime implicants on the joint map. The joint essential prime implicants are shown in green.
- Prime Implicants: 7
- Distinguished 1-Cells: 7
- Essential Prime Implicants: 4
- Minimal Sums: 2
Y = A'B'C' + BE + ABC' + ACE + A'DE
Y = A'B'C' + BE + ABC' + ACE + CDE
Note that the joint map can help you identify the joint prime implicants.
6-Variable Karnaugh Maps
The prime implicants unique to each map are shown in black.
The prime implicants shared between maps 0 and 1 (A=0) are shown in aqua.
The prime implicants shared between maps 0 and 2 (B=0) are shown in violet.
The prime implicants shared between maps 1 and 3 (B=1) are shown in olive.
The prime implicants shared between maps 2 and 3 (A=1) are shown in brown.
The prime implicants shared between all 4 maps are shown in orange.
To find the prime implicants shared among maps it may help to draw out each of the 5 joint maps.
- Distinguished 1-Cells: 10
- Essential Prime Implicants: 5
- Minimal Sums: 2
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- Essential Prime Implicants
- A'EF (Maps 0 & 1)
BCD' (Maps 1 & 3)
B'D'F' (Maps 0 & 2)
ACE' (Maps 2 & 3)
ABDE' (Map 3)
Y = A'EF + BCD' + B'D'F' + ACE' + ABDE' + B'DE'F + A'B'C'F
Y = A'EF + BCD' + B'D'F' + ACE' + ABDE' + B'DE'F + A'B'C'D'
Source:http://web.cecs.pdx.edu/~mcnames/ECE171/Lectures/Lecture10.html
