Circuits, Truth Tables & Boolean Algebra
Expressions Can describe circuits in terms of Boolean expression
Expressions Write Q as a function of A, B and C
Expressions Write Q as a function of A, B and C
Expressions Write Q as a function of A, B and C
Expressions Write Q as a function of A, B and C
Where We Are… Can represent a circuit's output with Boolean expression: AB + AC
Where We Are… We can simplify boolean expressions AB + AC A(B + C)
Where We Are… Thus we can simplify circuits AB + AC A(B + C)
Sum Of Products Can convert any truth table to expression – Identify ways to get 1 output X = 1 if red OR green OR yellow
Sum Of Products
Multiple Inputs
SOP Circuit
Implication 1 Can build circuit from SOP expression: Any circuit can be build with NOT, AND & OR
And… Can make NOT, AND & OR with only NAND NOT ANDOR
Implication 2 Any circuit can be build with NAND gates only…
Implication 2 Replace NOT with NAND
Implication 2 Put inversion bubbles out of AND & into OR – 2 negations cancel out
Implication 2
SOP Circuit Can build circuit from SOP expression… … but can often do better…
Logisim Build simplified circuit from truth table… – Window Combinational Analysis Build truth table for circuit… – Project Analyze Circuit
Simplification
Multiple Outputs Multiple outputs – Each output separate function/circuit INOUT ABXY
Multiple Outputs Multiple outputs – Each output separate function/circuit X = AB INOUT ABXY
Multiple Outputs INOUT ABXY
Multiple Outputs