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Simplify to minimum SOP using a Karnaugh map (Sigma the typical symbol for a summation is not available in canvas so we are using S for summation, m means minterm, and d means don’t cares) F(A,B,C,D) = Sm( 0,1,2,8,11,15) + Sd(9,10,14)

Simplify this to a minimum SOP ((EF)’+AB+C’D’)EF

Simplify this expression to a minimum SOP (A’C+B+D+E)(A’C+D)’

Find the dual of  a(b+c)=ab+ac

Consensus xy + yz + x’z = xy + x’z Using consensus and other properties simplify to minimum SOP Remember consensus can be used to add a term too XY+X’YZ’+YZ

Consensus xy + yz + x’z = xy + x’z Using consensus and other properties simplify to minimum SOP ABC + A’BD + BCD

Simplify this expression as much as possible Consensus xy + yz + x’z = xy + x’z Using consensus and other properties simplify to minimum SOP BC’D’+ABC’+AC’D+AB’D+A’BD’

All valid Boolean expressions have a dual, an expression and it’s dual may not be equal but they are both true True or False?

Consensus xy + yz + x’z = xy + x’z Using consensus and other properties simplify to minimum SOP Remember consensus can be used to add a term too XY+X’YZ’+YZ