Thursday, 9 February 2012

Minimization using boolean algebra laws


Theorems of Boolean algebra (consensus theorem, involution theorem etc.) can be used to minimize the Boolean expressions. But it depends on experience of the designer to identify correct law that can be applied in a particular situation.
Ex: minimize a’b’c’+a’bc’+a’bc+abc’
a’b’c’+a’bc’+a’bc+abc’=a’c’(b’+b)+a’bc+abc’
                                          =a’c’+a’bc+abc’
                                          =a’(c’+bc)+abc’
                                          =a’((c’+c)(c’+b))+abc’
                                          =a’(c’+b)+abc’
                                          =a’c’+a’b+abc’
                                          =a’c’+b(a’+ac’)
                                          =a’c’+b((a’+a)(a’+c’))
                                          =a’c’+b(a’+c’)
                                          =a’c’+a’b+bc’

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