Wednesday, 8 February 2012

Boolean functions


  • with ‘n’ variables, no. of different switching functions possible are 2^(2^n)
  • example, if n=2 variables then total possible functions are 16
SOP and POS forms:
SOP and POS forms of the function are not unique
SOP (sum of products) form: function is represented as OR of AND terms
Ex: ab + bc + ca
POS (product of sums) form: functions is represented as AND of OR terms
Ex: (a+b)(b+c)(c+a)

Canonical form:
Canonical SOP & POS forms are unique for each function
Min term: in a function of ‘n’ variables, if a product term contains each of ‘n’ variables in true or complemented form in exactly one time, the product term is called min term.
Ex: 3 variable function m0=a’b’c’, m1= a’b’c
Max term: in a function of ‘n’ variables, if a sum term contains each of ‘n’ variables in true or complemented form in exactly one time, the sum term is called max term
Ex: 3 variable function M0=a+b+c, M1=a+b+c’
Canonical SOP form: function consists of sum of min terms only
Ex: f(a,b,c)=a’bc’+abc+a’b’c’
Canonical POS form: function consists of products of max terms only
Ex: f(a,b,c)= (a+b+c)(a+b+c’)(a’+b+c)(a’+b+c’)

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