L17 Digital Computation

L17 Digital Computation - EE 40 Digital Computation Boolean...

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EE 40 Digital Computation Boolean Algebra EE 40 Lecture 17: Digital Computation 1
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Skills! Write truth tables (TTs), e.g. adder Derive Boolean expression for TT (sum of products) Convert Boolean expressions (de Morgan’s rule) Implement Boolean expressions with logic gates Synthesize Boolean functions with switches / transistors Calculate input capacitance and output resistance for CMOS gates, relate to XTR dimensions (W, L) Calculate delay and energy consumed by CMOS gates Estimate power of digital (CMOS) circuits based on # of gates, clock speed, supply voltage EE 40 Lecture 17: Digital Computation 2
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Boolean Algebra Computation with binary (2-valued) signals Truth table Example: 1 input, 1 output EE 40 Lecture 17: Digital Computation 3 D i D o 0 1 D i D o 0 1 Inverter (NOT) Identity
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Boolean Operators with Two Inputs EE 40 Lecture 17: Digital Computation 4 D o D i AND OR XOR NAND NOR 00 01 10 11
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NOT AND NAND OR XOR Boolean Operators EE 40 Lecture 17: Digital Computation 5
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Boolean Algebra (Examples) A + 1 = 1 A ∙ 0 = 0 A ∙ 1 = A ∙ (B + C) = (A ∙ B) + (A ∙ C) Check with truth table EE 40 Lecture 17: Digital Computation 6
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De Morgan’s Rules EE 40 Lecture 17: Digital Computation 7 Example: realize using only NAND operators
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Application: Binary Addition EE 40 Lecture 17: Digital Computation 8 A 0 1 0 1 B 0 1 1 0 C 0
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