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Boolean Algebra

Boolean Equations: Different forms

Standard form: In a standard form we don’t have to compulsorily write all the literals in all the terms of an expression.

e.g. f = xyz + y + x

 f = x’y’z’ + x’yz

f= xy + x’y’

Canonical form: In a canonical form we have to compulsorily write all the literals in all the terms of an expression.

e.g. xyz+x’y’z+x’y’z’

xy+yz+x’y’ (for 2 variables)

x+y (for 1 variable)

xyz+xyz’

but xy + x & xyz+x’yz+xz are not a canonical term (as in last terms of both expressions we don’t have all the literals)

We can represent the expressions using min terms or max terms but we first convert standard form of expression to canonical form and then we write the expression in terms of min or max terms

Q- f= xyz+xy’

f=xyz+xy’.1 = xyz + xy’. (z+z’) = xyz + xy’z + xy’z’ = m7 + m5 + m4 = ∑(4, 5, 7)

Sum of products: It is a Boolean expression where different AND terms are ORed. It is denoted by SOP

e.g.  xyz+x’y’z+x’y’z’

xy + x’y’

xyz + y + x

Product of sums: It is a Boolean expression where different OR terms are ANDed. It is denoted by POS

e.g. (y+x’) (x+z) (y+z)

(y+x’+z’) (x+z+y) (x+z+y’)

e.g.  (xy + x’y)  (x’y’+ xy) which out of the above 2 forms is it represented in?

Ans: none. It is neither SOP nor POS

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