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Digital Logic Gates Sum of Products (Review) Procedure: 1. Form a minterm for each combination of the variables that produces a 1 2. OR all the minterms. Three-Terminal AND Gate F2 A B C 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 1 1 1 1 𝑓1 = 𝐴 ∙ 𝐵 ∙ 𝐶 = 𝐴 ∙ 𝐵 ∙ 𝐶 = 𝐴 ∙ 𝐵 ∙ 𝐶 = 𝐴 ∙ 𝐵 ∙ 𝐵 ∙ 𝐶 = 𝐴 ∙ 𝐵 ∙ 𝐵 ∙ 𝐶 Application of Sum of Products 𝑓1 = 𝐴 ∙ 𝐵 ∙ 𝐶 = 𝐴 ∙ 𝐵 ∙ 𝐶 = 𝐴 ∙ 𝐵 ∙ 𝐶 = 𝐴 ∙ 𝐵 ∙ 𝐵 ∙ 𝐶 = 𝐴 ∙ 𝐵 ∙ 𝐵 ∙ 𝐶 Digital Logic Gates 2-Input AND Gate NAND INV NAND INV 2-Input OR Gate NOR INV NOR INV Universal Gates • NAND and NOR are easier to build than AND and OR • NAND and NOR are used to implement AND and OR gates NAND/NOR NAND-Based OR Gate NOR-Based NAND Gate XOR/XNOR F=1 when x≠y F=1 when x=y Application of an XOR Gate Use a XOR to Generate PseudoRandom Numbers Reference: http://en.wikipedia.org/wiki/Linear_feedback_shift_register logic.ly/demo Circuit Simplification Example Solution Factoring—the first & third terms above have AC in common, which can be factored out: Since B + B = 1, then… z = A(C + B) Topics for Quiz 1 • Date: 3/8/2012 – In class – No Make-Up • • • • • • • • • Number Conversion Arithmetic Operations Complements Signed Binary Numbers Addition/Subtraction Boolean Algebra Logic Gates Sum of Products Circuit Simplifications Example 1 Example 2