Write a program in Python to convert standard POS(product of sums) form to standard SOP(sum of products) form.
Assumptions: The input POS expression is standard. The variables in POS expression are continuous i.e. if expression contains variable A then it will have variables B, C respectively and each Sum term contains the alphabets in sorted order i.e. A + B + C (not like B+A+C).
Input : (A + B + C).(A + B + C').(A + B' + C).(A' + B + C) Output : A'BC + AB'C + ABC' + ABC Input : (A + B).(A' + B') Output : A'B + AB'
- First of all convert each sum term to its equivalent binary form. For example, if (A+B+C’) then take 0 for uncomplement variable(A, B) and take 1 for complement variable(C) so binary conversion is 011) and then finally equivalent to its decimal form(for ex: 001 = 1) and store in a list.
- Now for SOP form take all those terms which are not present in the list formed in step 1st and then convert each term to binary and hence change to POS form. For example –
Suppose 4 was not in the list then 5==> 101 (binary)
Now, replace 0 by complement variables(B)
replace 1 by uncomplement variables(A, C)
101 ==> AB’C
After each individual sum term use ‘+’
Below is the Python implementation of above approach:
Standard SOP form of (A+B+C).(A+B+C').(A+B'+C).(A'+B + C) ==> A'BC+AB'C+ABC'+ABC Standard SOP form of (A + B).(A'+B') ==> A'B+AB'
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