chap1 - ELEC151 Digital Circuits and Systems Lecture Note...

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ELEC151 Digital Circuits and Systems Ho-Chi Huang, Lecture Notes, No. 1-1 Lecture Note #1 Introduction • Design Representations – 7 ways to represent a same design – Truth table, Boolean algebra, logic gates, logic blocks, behaviors waveforms, and switches • Digital Integrated Circuits – Complementary MOS (CMOS) --- 10-7, 10-8 --- – Circuit Characteristics --- 10-1, 10-2 --- • Binary Systems – A quick overview of all 9 sections --- Chapter 1 --- • Reading Assignments: – Chapter 1 – Section 10-1, 10-2, 10-7, 10-8 ELEC151 Digital Circuits and Systems Ho-Chi Huang, Lecture Notes, No. 1-2 The Elements of Modern Design Rapid Prototyping Technologies Design Representations Circuit Technologies TTL MOS CMOS BiCMOS Truth Tables Boolean Algebra Logic Gates Logic Blocks Behaviors Waveforms Simulation Synthesis ROM PAL PLA SPLD CPLD FPGA Computer-Aided Design Representations, Circuit Technologies, Rapid Prototyping ELEC151 Digital Circuits and Systems Ho-Chi Huang, Lecture Notes, No. 1-3 Example: half adder adds two binary digits to form Sum and Carry Example: full adder adds two binary digits and Carry in to form Sum and Carry Out A B 0 0 1 1 0 1 0 1 Sum Carry 0 1 1 0 0 0 0 1 A 0 0 0 0 1 1 1 1 B 0 0 1 1 0 0 1 1 C in 0 1 0 1 0 1 0 1 S um 0 1 1 0 1 0 0 1 C out 0 0 0 1 0 1 1 1 Representations of a Digital Design • Truth Table – tabulate all possible input combinations and their associated output values ELEC151 Digital Circuits and Systems Ho-Chi Huang, Lecture Notes, No. 1-4 A B Sum Carry 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 1 Sum = A’ B + A B’ Carry = A B Representations of a Digital Design • Boolean Algebra – values: 0, 1 – variables: A, B, C, . . ., X, Y, Z – operations: NOT, AND and OR • Notation – NOT X is written as X’ – X AND Y is written as X • Y, or sometimes X Y – X OR Y is written as X + Y • Deriving Boolean equations from truth tables:
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ELEC151 Digital Circuits and Systems Ho-Chi Huang, Lecture Notes, No. 1-5 Representations of a Digital Design A 0 0 0 0 1 1 1 1 B 0 0 1 1 0 0 1 1 Cin 0 1 0 1 0 1 0 1 Sum 0 1 1 0 1 0 0 1 Cout 0 0 0 1 0 1 1 1 Sum = A’ B’ Cin + A’ B Cin’ + AB’ Cin’ + A B Cin Cout = A’ B Cin + A B’ Cin + A B Cin’ + A B Cin Two equations can also REPRESENT a full adder We will learn more of Boolean Algebra in Chapter 2 Two equations can also REPRESENT a full adder We will learn more of Boolean Algebra in Chapter 2 • Boolean Algebra: another example for full adder ELEC151 Digital Circuits and Systems Ho-Chi Huang, Lecture Notes, No. 1-6 • Laws of Boolean Algebra – Reducing the complexity of Boolean equations • Why Logic Minimization? – Cost, Power (and Speed) are improved Cout = A Cin + B Cin + A B A 0 0 0 0 1 1 1 1 C in 0 1 0 1 0 1 0 1 B 0 0 1 1 0 0 1 1 C out 0 0 0 1 0 1 1 1 B C in A C in A B Representations of a Digital Design We will learn more about gate-level logic minimization in Chapter 3 We will learn more about gate-level logic minimization in Chapter 3 ELEC151 Digital Circuits and Systems Ho-Chi Huang, Lecture Notes, No. 1-7 Representations of a Digital Design Gate Symbols Half Adder Schematic Inverter AND OR Net 1 Net 2 A B CARR Y SUM
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