ECE 124 Digital Circuits and Systems Winter 2011 Introduction Calendar Description:

Transcription

1 ECE 124 Digital Circuits and Systems Winter 2011 Introduction Calendar Description: Number systems. Switching algebra. Hardware description languages. Simplification of Boolean functions. Combinational logic, sequential logic, state machines; their design and implementation. Timing considerations. Implementation technologies. 1

2 Course Information Instructor Dr. Otman Basir (Ext Room E5 5116) Dept. of Electrical & Computer Engineering University of Waterloo Course web site: Lab Instructors: Eric Praetzel Teaching Assistants: 1) Haitham Amar E Ext ) David Li E ) Si-Yun Li E ) Yusra Maatug E ) Jean-Luc Francois-Xavier Orgiazzi EIT-3119 Ext )Tabibiazar, Arash E )Zheng, Lin 8)Jianchen Tao 2

3 Course Information Text Book M. Morris Mano, Digital Design, 3 rd or 4 th Edition, Prentice Hall Lecture Notes: Laboratory manual Download from Marking Scheme Labs 30%; Midterm 20%; Final 50% To pass the course, your Labs mark should be higher than 50% of the max Labs mark. 3

4 Course Objectives Class Objectives: Study the basic concepts of binary number systems and binary algebra Learn the basic circuit forms (combinational, sequential, state machine) Learn the principles of digital circuit optimization Laboratory Objectives: Acquire familiarity with basic digital logic chips Learn good digital circuit design, wiring, and debugging habits Learn the use of digital circuit simulators and design tools Learn how to use more advanced digital logic devices to greatly simplify circuit design and development. 4

5 Course Information - Labs 5

6 Topics to be covered: Introduction This Lecture Boolean Algebra, Logic Gates & Simplification Theorems, functions, canonical & standard forms, Digital logic gates, Logic simplification Karnaugh map, sum of products, product of sums, don t cares Combinational Logic Design Analysis procedure, Design procedure, Adders, Subtractors, Decoders, Encoders, etc. Sync. Async, Seq. Logic, Registers, Counters Latches and flip-flops, Analysis, State reduction, Design procedure, Registers, Ripple counters, Synchronous counters Memory & Programmable Logic RAM, ROM, PLA, PAL, FPGAs 6

7 Relationship with Future Courses ECE124provides the foundation for higher order digital systems & digital integrated circuit courses ECE xxx - Digital computers ECE xxx Microprocessor Systems & Interfacing ECE xxx Digital Systems Engineering ECE xxx Digital Integrated Circuits ECE xxx Integrated VLSI Systems 7

8 MIDTERM EXAM TUESDAY FEB. 15 TH, :00-3:00 THIS FRIDAY! 8

9 INTRODUCTION 9

10 Hierarchy of Computation Problem Algorithm s Programming in High-Level Language Compiler/Assembler/ Linker Instruction Set Architecture (ISA) Binary Micro-architecture Functional units/ Building blocks Gates Level Design Transistors Target Machine (one implementation) System architecture Manufacturing 10 Human Level System Level RTL Level Logic Level Circuit Level Silicon Level

11 Digital Hardware In this course we will discover there are different types of parts we can use to implement a digital system. Standard Parts. Ready off the shelf components implementing specific functions. Might connect them together on a PCB to get an entire design. OR,AND,MUX,DECODER, ETC Programmable Logic Devices (FPGAs and CPLDs). Generic Parts that we can program (sometimes multiple times) to implement complex circuits. Large and expensive (unit cost). Sometimes slow. Fast time to market. Custom Chips ASICs. Entirely custom or semi-custom design. High startup costs (millions of $$$). Long turn around. Good for volume production (i.e., need lots of them!). Source: E&CE 223 Digital Circuits and Systems (A. Kennings) Page 11

12 Design Flows We will hopefully discover that digital design can be complicated and we need to use software tools and a design methodology to be successful. There are different types of design Functional design What should the circuit do? Do we get correct outputs given inputs? Might do a lot of simulations here Physical design This is actually making the digital system. Will need to do further simulations and check timing, etc. E&CE 223 Digital Circuits and Systems (A. Kennings) Page 12

13 Functional Design This is where, using a bunch of different design methods, we try to obtain a description that operates according to our initial design objectives; are the outputs correct given the inputs? Desired Product/ Idea Design Specification This is functional because we are not necessarily taking into account details of the final physical implementation (e.g., like resistance and capacitance). Other... Schematic Verilog VHDL Other... Aldec ModelSim Initial Design Simulation Function Correct? Redesign E&CE 223 Digital Circuits and Systems (A. Kennings) Page 13

14 Sketch of Physical Design Here we seek a physical implementation; prior to this step, we know the our description behaves correctly in terms of its functionality. In physical design, we must pay attention to realities like timing, power, heat, etc. Other... Cadence Synopsys Altera Xilinx Implementation Partitioning Synthesis/Technology Mapping Placement/Routing Meets Timing? Corrections Minor Errors The physical design flow can vary slightly depending on the target implementation technology. E&CE 223 Digital Circuits and Systems (A. Kennings) Page 14

15 The Computing Cycle Application Domain Complex: Quantities Relationships Operations Temporal Spatial Digital Domain Binary Quantities (zeros and ones) Logical Operators (Subject to the rules of Boolean algebra) 15

16 Application Domain Complex: Quantities Relationships Operations Temporal Spatial Digital Domain Binary Quantities (zeros and ones) Logical Operators (Subject to the rules of Boolean algebra) Information Representation: Numbers, TEXT, OPERATIONS, ETC.? 16

17 Number Representation A decimal number such as 7392 represents 7392 = 7x x x x10 0 It is practical to write only coefficients and deduce power of 10s from position In general, any radix (base) can be used Define coefficients a i in radix r 0 <= a i <r a n r n + a n-1 r n-1. a 0 r a -m r -m Common radics r = 2, 4, 8, 10, 16 17

18 General Radix Representation r = 10 (Dec.) r = 2 (Binary) r = 8 (Octal) r = 16 (Hex) A B C D E F 18

19 Conversion between Binary/Octal/Hex Nice simple ways to convert between these three number systems, since all are a power of 2 Binary to Octal simply requires grouping bits into groups of 3-bits and converting Binary to Hex simply requires grouping bits into groups of 4- bits and converting Going the other direction (Octal to Binary or Hex to Binary) should follow Example ( ) 2 = (4745) 8 ( ) 2 = (9E5) 16 19

20 Complements In computers, the representation and manipulation of ve numbers is often performed using complements Complements for a radix come in two forms R s complement (Radix complement) (r-1) s complement (Diminished radix complement) For binary system -- 2 s complement, & 1 s complement 20

21 r s Complement Given a +ve number N with n digits N = (a n-1 a n-2..a 0 ) r s complement is defined as r n N for N 0; zero otherwise Examples 10 s complement (37218) 10 = = ( ) 10 = = Examples 2 s complement (101110) 2 = = (0.0110) 2 = =

22 (r-1) s Complement Given a +ve number N with n digit integer part & m digit fractional part N = (a n-1 a n-2..a 0..a -1 a - 2.a -m ) (r-1) s complement is defined as r n r -m - N Examples 9 s complement (37218) 10 = = ( ) 10 = = Examples 1 s complement (101110) 2 = = = (0.0110) 2 = = =

23 Interesting Facts The complement of a complement returns the original number Since we work with binary numbers a lot in digital systems, it is really worth noting that: The 1 s complement of a number is obtained by flipping bits The 2 s complement of a number is obtained by flipping bits and adding 1 23

24 Signed Numbers Computers handle signed numbers as well Numbers are represented in a fixed # of bits Often required to represent both +ve & -ve numbers in the same n-bit format Left most bit (Most Significant Bit) represents the sign 0 +ve; 1 -ve Three common representations Sign & magnitude Signed 1 s complement Signed 2 s complement For +ve numbers, all three have same representation 24

25 1. signed magnitude In each case: left-most bit indicates sign: positive (0) or negative (1). Consider 1. signed magnitude: = = Sign bit Magnitude Sign bit Magnitude

26 2. One s Complement Representation The one s complement of a binary number involves inverting all bits. To find negative of 1 s complement number take the 1 s complement of whole number including the sign bit = = Sign bit Magnitude Sign bit 1 complement

27 3. Two s Complement Representation The two s complement of a binary number involves inverting all bits and adding 1. To find the negative of a signed number take the 2 s the 2 s complement of the positive number including the sign bit = = Sign bit Magnitude Sign bit 2 s complement

28 Sign addition in 2 s complement The rule for addition is add the two numbers, including their sign bits, and discard any carry out of the sign (leftmost) bit position. Numerical examples for addition are shown below. Example: In each of the four cases, the operation performed is always addition, including the sign bits. Only one rule for addition, no separate treatment of subtraction. Negative numbers are always represented in 2 s complement.