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tutorial5_4 - Elec 151 Tutorial#5 Binary Code Gray Code 4...

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1 Outline : •Karnaugh Maps - Problems - Sum of Products (SOP) and Product of Sums (POS) • Lab 4: Combinational Logic Gates - Design and implementation (design flow) - A Design Example Elec Elec 151 Tutorial #5 151 Tutorial #5 Tutorial #5 2 Gray Binary 0 0 0 0 1 1 0 0 1 1 0 0 0 0 1 0 1 1 0 1 1 1 0 0 0 0 1 1 0 0 1 1 0 0 0 0 1 0 1 1 0 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 0 0 1 0 1 0 1 1 0 0 1 0 1 1 1 1 0 0 1 1 1 0 1 0 1 0 1 1 1 1 0 0 1 0 1 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 Binary Code & Gray Code 4 bits 0 1 3 2 4 5 7 6 8 9 11 10 12 13 15 14 A Gray Code has the property that adjacent codewords differ in only one position . 1 1 1 1 1 1 0 0 3 Z A 0 0 1 0 1 1 0 0 1 0 B B A B A Z + = B A = XOR Z A 0 0 1 0 1 1 0 1 0 1 B AB B A Z + = B A B A = = XNOR Exclusive OR and Exclusive NOR See : Z = 0 when A=B See : Z = 1 when A=B B Z A B Z A ringbutton2 ___ B A B A A XNOR B = = See: 1 1 1 0 4 Converting Boolean expressions to XOR gates ___ ___ ___ ___ ___ C B A C B A C B A ABC Z + + + = Example 1 Example 2 Using the first expression in Example 1, proof that ) ( ) ( ) ( C A B C B A C B A = =
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5 More Problems Using Boolean algebra, verify that the schematic shown below implements an XOR function.
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