Boolean Algebra Cheat Sheet, Cheat Sheet of Algebra

Download Boolean Algebra Cheat Sheet and more Cheat Sheet Algebra in PDF only on Docsity! Boolean Algebra Steps to Solution (SOP) 1. From the problem statement a truth table is formed. The problem may be expressed in words, waveforms, tables, Boolean expressions, or as a circuit. The problem statement must specify (a) the number of inputs, and (b) the desired output for all input conditions. With this information in hand the problem is synthesized into a set of input and corresponding output conditions in tabular form (a truth table). 2. A column is added to the truth table and named product terms. For each row whose output is 1, a product term is formed from the input columns. 3. A sum-of-products (SOP) expression is built from these product terms. 4. The algebraic expression is simplified 5. The answer is checked. 6. A logical circuit is designed. Boolean Operators INPUT OUTPUT NOT OR AND Logical Operators x y x or x' x+y xy Traditional Representation ~x x|y x&y Bitwise HDL Verilog 0 0 1 0 0 0 1 1 0 1 0 0 1 0 1 1 1 1 Basic Laws and Theorems of Boolean Algebra Law Dual (D) 1 x x Involution OR Laws AND Laws 2 xx  0 xx 1 Identity element under addition is 0 and under multiplication it is 1 3 11x 00 x Dominance 4 x x x  x x x  Idempotent 5 1 xx x x  0 Complements Commutative 6 x y y x   x y y x   Associative 7 zyxzyx  )()( x yz xy z( ) ( ) Distributive 8 x y z xy xz( )   x yz x y x z   ( )( ) Theorem Simplification 9 x xy x  x x y x( )  Absorption 10 x xy x y   x x y xy( )  Degenerate-Reflect Law De Morgan’s 11 x y x y   x y x y  