chap1(4_in_1)

chap1(4_in_1) - ELEC151 Digital Circuits and Systems...

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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 Switches 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 Design Representations – Truth Table • Truth Table – tabulate all possible input combinations and their associated output values We will learn more about half adder, full adder and other binary adders in Section 4-4 on Page 119 We will learn more about half adder, full adder and other binary adders in Section 4-4 on Page 119 A +B Carry Sum A B +C i n Cout Sum 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 Design Representations – Boolean Equations • 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: We will learn more about Boolean Algebra in Chapter 2 We will learn more about Boolean Algebra in Chapter 2
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ELEC151 Digital Circuits and Systems Ho-Chi Huang, Lecture Notes, No. 1-5 Design Representations – Boolean Equations 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 Boolean equations can also represent a full adder. We will learn more about Boolean Algebra in Chapter 2 Two Boolean equations can also represent a full adder. We will learn more about 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?
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chap1(4_in_1) - ELEC151 Digital Circuits and Systems...

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