# Minimal to Canonical Form Conversion

• Difficulty Level : Expert
• Last Updated : 02 Jun, 2020

Canonical Form is also called standard form, we directly obtained it from truth table and hence we have all the variable in normal or complimented form in each minterm.

There are 3 steps for conversion of minimal form to canonical form.

• Find the Total Number of variable present in minimal form.
• Find the variables absent in each minterm.
• Try to apply operation for converting min to canonical term using one(1) or zero(o) logic.

• Conversion of Sum of Products (SOP) form to Canonical Form –
Set of rules are same as stated above.

Example-1:

```Input :
Y=A+B'C
Output :
(A.B.C)+(A.B.C')+(A.B'.C)+(A.B'.C')+(A'.B'.C) ```

Explanation –

• Step-1:
Find the Total Number of variable present in minimal form like in this variables present are A, B, C.
• Step-2:
Find the variables absent in each term like in this in this variable absent in minterm(0) is B and C and variable absent in minterm(1) is A.
• Step-3:
Try to apply operation for converting min to canonical term using one(1) or zero(o) logic, In this case it is SOP form so we AND one(1) to each minterm where variables are absent in simple term if we multiply each minterm by one(1) then there is no effect on resultant equation so in this case, after that we replace one(1) by Sum (Variable +Complement of variable) then use Properties of switching algebra to solve further.

Conversion steps –

```= A+B.C
= (A.1)+(B.C.1)
= (A.(B+B'))+((A+A').(B.C))
= ((A.B.C)+(A.B.C')+(A.B'.C)+(A.B'.C')+(A'.B'.C))  ```

Conversion of Product of Sums(POS) form to Canonical Form –
Set of rules are same as stated above.

Example-2:

```Input :
Y=(A+B+C).(A'+C)

Output :
(A+B+C').(A'+C+B).(A'+C+B') ```

Explanation –

1. Step-1:
Find the Total Number of variable present in minimal form like in this variables present are A, B, C.
2. Step-2:
Find the variables absent in each term like in this in this variable absent is C in maxterm(1)
3. Step-3:
Try to apply operation for converting minimal to canonical term using one(1) or zero(o) logic, In this case it is POS form so we OR zero(0) to each maxterm where variables are absent in simple term if we add each maxterm by zero(0) then there is no effect on resultant equation so in this case, after that we replace zero(0) by Product(Variable * Complement of variable) then use Properties of switching algebra to solve further.

Conversion steps –

```= (A+B+C).(A'+B)
= (A+B+C').(A'+(B.B')+C)
= (A+B+C').(A'+C+B).(A'+C+B') ```
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