Lecture5-Simplification - E1.2 Digital Electronics 1 5.1 31...

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E1.2 Digital Electronics 1 5.1 31 October 2008 Lecture 5: Logic Simplification & Karnaugh Maps Dr Pete Sedcole Department of E&E Engineering Imperial College London http://cas.ee.ic.ac.uk/~nps/ (Floyd 4.5 – 4.10) (Tocci 4.1 – 4.5) E1.2 Digital Electronics 1 5.2 31 October 2008 In this lecture: Standard form of Boolean Expression: – Sum-of-Products & Product-of-Sums (SOP/POS) – Canonical form Boolean simplification with Boolean algebra Boolean simplification with Karnaugh Maps The “Don’t care” logic state E1.2 Digital Electronics 1 5.3 31 October 2008 Forms of Boolean Expressions Sum-of-products (SOP) – e.g.: X = ABC + DEF + AEF – the product (AND) terms are formed first, then summed (OR) Product-of-sums (POS) – e.g.: Y = (A+B+E)(C+D+E)(B+F) – the sum (OR) terms are formed first, then the product (AND) It is possible to convert between the two forms using DeMorgan’s theorems. E1.2 Digital Electronics 1 5.4 31 October 2008 Canonical form In the canonical form of a Boolean expression, every variable appears in every term – e.g.: Canonical form is not an efficient way of writing the Boolean expression, but is useful sometimes in design and analysis D C B A CD B A D C AB D C B A f + + = ) , , , (
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