The QuineMcClusky Method of Logic Reduction
The QuineMcClusky method is an algorithm for reducing a logic equation to its simplest reduced form. For anything but the most straight forward of equations, it can be an impressive timesaver when compared to other techniques such as traditional algebraic reduction and Karnaugh maps. It also has the advantage of being easily implemented with a computer or programmable calculator.
Hi, I'm still working on this. it is not ready yet.
Typically, the need to employ logic reduction comes from having a truth table and wanting to implement it in the real worlddiscrete logic, array logic, inside of a computer program, or whatever else your mind can dream up. The truth table is constructed by known what result is desired for a combinartion of inputs and outputs:
DBCA  Q 
0000  1 
0001  0 
0010  0 
0011  1 
0100  0 
0101  0 
0110  1 
0111  1 
1000  1 
1001  0 
1010  0 
1011  1 
1100  1 
1101  0 
1110  1 
1111  1 
The above truth table was made up randomly. The equation for it is:
Q = ~A~B~C~D + ~A~BCD + ~ABC~D + ~ABCD + A~B~C~D + A~BCD + ABC~D + ABCD
Here, a tilde (~) before a term indicates negation.
Reduction Step 1
Extract all the input combinations that produce a true result:
DBCA  Q 
0000  1 
0011  1 
0110  1 
0111  1 
1000  1 
1011  1 
1100  1 
1110  1 
1111  1 
Reduction Step 2
Rearrange the rows so that the are sorted by the number of ones contained in the inputs:
DBCA  Q  # of 1's 
0000  1  0 
1000  1  1 
0011  1  2 
1100  1  2 
0110  1  2 
0111  1  3 
1011  1  3 
1110  1  3 
1111  1  4 
Reduction Step 3
This is the tricky step. Try to match each item in each group of ones with each item in the following group. If there is a one bit difference, replace that bit with an "X" and write it in a new table. If there are no matches that have a one bit difference, simply transfer the origial item to the new table. For example:
Matching 0 groups with 1 groups, we get:
DBCA  Q  # of 1's 
X000  1  0 
X000  1  1 
X011  1  2 
1100  1  2 
011X  1  2 
011X  1  3 
X011  1  3 
111X  1  3 
111X  1  4 
Reduction Step 4
Reduce the redundant groups:
DBCA  Q  # of 1's 
X000  1  0 
X011  1  2 
1100  1  2 
011X  1  2 
111X  1  4 
Reduction Step 4
Repeat the reduction process:
DBCA  Q  # of 1's 
X000  1  0 
X011  1  2 
1100  1  2 
X11X  1  2 
Reduction Step 4
Repeat the reduction process:
DBCA  Q  # of 1's 
X000  1  0 
XX1X  1  2 
1100  1  2 
