Lecture 3 Processor: Datapath and Control
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Chapter 3: Combinational Logic Design
Chapter 3: Combinational Logic Design 1 Introduction • We have learned all the prerequisite material: – Truth tables and Boolean expressions describe functions – Expressions can be converted into hardware circuits – Boolean algebra and K-maps help simplify expressions and circuits • Now, let us put all of these foundations to good use, to analyze and design some larger circuits 2 Introduction • Logic circuits for digital systems may be – Combinational – Sequential • A combinational circuit consists of logic gates whose outputs at any time are determined by the current input values, i.e., it has no memory elements • A sequential circuit consists of logic gates whose outputs at any time are determined by the current input values as well as the past input values, i.e., it has memory elements 3 Introduction • Each input and output variable is a binary variable • 2^n possible binary input combinations • One possible binary value at the output for each input combination • A truth table or m Boolean functions can be used to specify input-output relation 4 Design Hierarchy • A single very large-scale integrated (VLSI) processos circuit contains several tens of millions of gates! • Imagine interconnecting these gates to form the processor • No complex circuit can be designed simply by interconnecting gates one at a time • Divide and Conquer approach is used to deal with the complexity – Break up the circuit into pieces (blocks) – Define the functions and the interfaces of each block such that the circuit formed by interconnecting the blocks obeys the original circuit specification – If a block is still too large and complex to be designed as a single entity, it can be broken into smaller blocks 5 Divide and Conquer 6 Hierarchical Design due to Divide and Conquer 7 Hierarchical Design • A hierarchy reduce the complexity required to represent the schematic diagram of a circuit • In any hierarchy, the leaves consist of predefined blocks, some of which may be primitives. -
On the Hardware Reduction of Z-Datapath of Vectoring CORDIC
On the Hardware Reduction of z-Datapath of Vectoring CORDIC R. Stapenhurst*, K. Maharatna**, J. Mathew*, J.L.Nunez-Yanez* and D. K. Pradhan* *University of Bristol, Bristol, UK **University of Southampton, Southampton, UK [email protected] Abstract— In this article we present a novel design of a hardware wordlength larger than 18-bits the hardware requirement of it optimal vectoring CORDIC processor. We present a mathematical becomes more than the classical CORDIC. theory to show that using bipolar binary notation it is possible to eliminate all the arithmetic computations required along the z- In this particular work we propose a formulation to eliminate datapath. Using this technique it is possible to achieve three and 1.5 all the arithmetic operations along the z-datapath for conventional times reduction in the number of registers and adder respectively two-sided vector rotation and thereby reducing the hardware compared to classical CORDIC. Following this, a 16-bit vectoring while increasing the accuracy. Also the resulting architecture CORDIC is designed for the application in Synchronizer for IEEE shows significant hardware saving as the wordlength increases. 802.11a standard. The total area and dynamic power consumption Although we stick to the 2’s complement number system, without of the processor is 0.14 mm2 and 700μW respectively when loss of generality, this formulation can be adopted easily for synthesized in 0.18μm CMOS library which shows its effectiveness redundant arithmetic and higher radix formulation. A 16-bit as a low-area low-power processor. processor developed following this formulation requires 0.14 mm2 area and consumes 700 μW dynamic power when synthesized in 0.18μm CMOS library. -
18-447 Computer Architecture Lecture 6: Multi-Cycle and Microprogrammed Microarchitectures
18-447 Computer Architecture Lecture 6: Multi-Cycle and Microprogrammed Microarchitectures Prof. Onur Mutlu Carnegie Mellon University Spring 2015, 1/28/2015 Agenda for Today & Next Few Lectures n Single-cycle Microarchitectures n Multi-cycle and Microprogrammed Microarchitectures n Pipelining n Issues in Pipelining: Control & Data Dependence Handling, State Maintenance and Recovery, … n Out-of-Order Execution n Issues in OoO Execution: Load-Store Handling, … 2 Reminder on Assignments n Lab 2 due next Friday (Feb 6) q Start early! n HW 1 due today n HW 2 out n Remember that all is for your benefit q Homeworks, especially so q All assignments can take time, but the goal is for you to learn very well 3 Lab 1 Grades 25 20 15 10 5 Number of Students 0 30 40 50 60 70 80 90 100 n Mean: 88.0 n Median: 96.0 n Standard Deviation: 16.9 4 Extra Credit for Lab Assignment 2 n Complete your normal (single-cycle) implementation first, and get it checked off in lab. n Then, implement the MIPS core using a microcoded approach similar to what we will discuss in class. n We are not specifying any particular details of the microcode format or the microarchitecture; you can be creative. n For the extra credit, the microcoded implementation should execute the same programs that your ordinary implementation does, and you should demo it by the normal lab deadline. n You will get maximum 4% of course grade n Document what you have done and demonstrate well 5 Readings for Today n P&P, Revised Appendix C q Microarchitecture of the LC-3b q Appendix A (LC-3b ISA) will be useful in following this n P&H, Appendix D q Mapping Control to Hardware n Optional q Maurice Wilkes, “The Best Way to Design an Automatic Calculating Machine,” Manchester Univ. -
Combinational Logic; Hierarchical Design and Analysis
Combinational Logic; Hierarchical Design and Analysis Tom Kelliher, CS 240 Feb. 10, 2012 1 Administrivia Announcements Collect assignment. Assignment Read 3.3. From Last Time IC technology. Outline 1. Combinational logic. 2. Hierarchical design 3. Design analysis. 1 Coming Up Design example. 2 Combinational Logic 1. Definition: Logic circuits in which the output(s) depend solely upon current inputs. 2. No feedback or memory. 3. Sequential circuits: outputs depend upon current inputs and previous inputs. Memory or registers. 4. Example — BCD to 7-segment decoder: S0 D0 S1 D1 BCD - 7 Seg S2 D2 S3 D3 Decoder S4 S5 S6 3 Hierarchical Design 1. Transistor counts: 2 Processor Year Transistor Count TI SN7400 1966 16 Intel 4004 1971 2,300 Intel 8085 1976 6,500 Intel 8088 1979 29,000 Intel 80386 1985 275,000 Intel Pentium 1993 3,100,000 Intel Pentium 4 2000 42,000,000 AMD Athlon 64 2003 105,900,000 Intel Core 2 Duo 2006 291,000,000 Intel Core 2 Quad 2006 582,000,000 NVIDIA G80 2006 681,000,000 Intel Dual Core Itanium 2 2006 1,700,000,000 Intel Atom 2008 42,000,000 Six Core Xeon 7400 2008 1,900,000,000 AMD RV770 2008 956,000,000 NVIDIA GT200 2008 1,400,000,000 Eight Core Xeon Nehalem-EX 2010 2,300,000,000 10 Core Xeon Westmere-EX 2011 2,600,000,000 AMD Cayman 2010 2,640,000,000 NVIDIA GF100 2010 3,000,000,000 Altera Stratix V 2011 3,800,000,000 2. Design and conquer: CPU ⇒ Integer Unit ⇒ Adder ⇒ binary full adder ⇒ NAND gates 3. -
Datapath Design I Systems I
Systems I Datapath Design I Topics Sequential instruction execution cycle Instruction mapping to hardware Instruction decoding Overview How do we build a digital computer? Hardware building blocks: digital logic primitives Instruction set architecture: what HW must implement Principled approach Hardware designed to implement one instruction at a time Plus connect to next instruction Decompose each instruction into a series of steps Expect that most steps will be common to many instructions Extend design from there Overlap execution of multiple instructions (pipelining) Later in this course Parallel execution of many instructions In more advanced computer architecture course 2 Y86 Instruction Set Byte 0 1 2 3 4 5 nop 0 0 addl 6 0 halt 1 0 subl 6 1 rrmovl rA, rB 2 0 rA rB andl 6 2 irmovl V, rB 3 0 8 rB V xorl 6 3 rmmovl rA, D(rB) 4 0 rA rB D jmp 7 0 mrmovl D(rB), rA 5 0 rA rB D jle 7 1 OPl rA, rB 6 fn rA rB jl 7 2 jXX Dest 7 fn Dest je 7 3 call Dest 8 0 Dest jne 7 4 ret 9 0 jge 7 5 pushl rA A 0 rA 8 jg 7 6 popl rA B 0 rA 8 3 Building Blocks fun Combinational Logic A A = Compute Boolean functions of L U inputs B 0 Continuously respond to input changes MUX Operate on data and implement 1 control Storage Elements valA A srcA Store bits valW Register W file dstW Addressable memories valB B Non-addressable registers srcB Clock Loaded only as clock rises Clock 4 Hardware Control Language Very simple hardware description language Can only express limited aspects of hardware operation Parts we want to explore and modify Data -
The Basics of Logic Design
C APPENDIX The Basics of Logic Design C.1 Introduction C-3 I always loved that C.2 Gates, Truth Tables, and Logic word, Boolean. Equations C-4 C.3 Combinational Logic C-9 Claude Shannon C.4 Using a Hardware Description IEEE Spectrum, April 1992 Language (Shannon’s master’s thesis showed that C-20 the algebra invented by George Boole in C.5 Constructing a Basic Arithmetic Logic the 1800s could represent the workings of Unit C-26 electrical switches.) C.6 Faster Addition: Carry Lookahead C-38 C.7 Clocks C-48 AAppendixC-9780123747501.inddppendixC-9780123747501.indd 2 226/07/116/07/11 66:28:28 PPMM C.8 Memory Elements: Flip-Flops, Latches, and Registers C-50 C.9 Memory Elements: SRAMs and DRAMs C-58 C.10 Finite-State Machines C-67 C.11 Timing Methodologies C-72 C.12 Field Programmable Devices C-78 C.13 Concluding Remarks C-79 C.14 Exercises C-80 C.1 Introduction This appendix provides a brief discussion of the basics of logic design. It does not replace a course in logic design, nor will it enable you to design signifi cant working logic systems. If you have little or no exposure to logic design, however, this appendix will provide suffi cient background to understand all the material in this book. In addition, if you are looking to understand some of the motivation behind how computers are implemented, this material will serve as a useful intro- duction. If your curiosity is aroused but not sated by this appendix, the references at the end provide several additional sources of information. -
Combinational Logic
MEC520 디지털 공학 Combinational Logic Jee-Hwan Ryu School of Mechanical Engineering Korea University of Technology and Education Combinational circuits Outputs are determined from the present inputs Consist of input/output variables and logic gates Binary signal to registers Binary signal from registers Sequential Circuits Outputs are determined from the present inputs and the state of the storage elements The state of the storage elements is a function of previous inputs Depends on present and past inputs Korea University of Technology and Education Analysis procedure To determine the function from a given circuit diagram Analysis procedure Make sure the circuit is combinational or sequential No Feedback and memory elements Obtain the output Boolean functions or the truth table Korea University of Technology and Education Obtain Procedure-Boolean Function Boolean function from a logic diagram Label all gate outputs with arbitrary symbols Make output functions at each level Substitute final outputs to input variables Korea University of Technology and Education Obtain Procedure-Truth Table Truth table from a logic diagram Put the input variables to binary numbers Determine the output value at each gate Obtain truth table Korea University of Technology and Education Example Korea University of Technology and Education Design Procedure Procedure to design a combinational circuit 1. Determine the required number of input and output from specification 2. Assign a symbol to each input/output 3. Derive the truth table from the -
LECTURE 5 Single-Cycle Datapath and Control
Single-Cycle LECTURE 5 Datapath and Control PROCESSORS In lecture 1, we reminded ourselves that the datapath and control are the two components that come together to be collectively known as the processor. • Datapath consists of the functional units of the processor. • Elements that hold data. • Program counter, register file, instruction memory, etc. • Elements that operate on data. • ALU, adders, etc. • Buses for transferring data between elements. • Control commands the datapath regarding when and how to route and operate on data. MIPS To showcase the process of creating a datapath and designing a control, we will be using a subset of the MIPS instruction set. Our available instructions include: • add, sub, and, or, slt • lw, sw • beq, j DATAPATH To start, we will look at the datapath elements needed by every instruction. First, we have instruction memory. Instruction memory is a state element that provides read-access to the instructions of a program and, given an address as input, supplies the corresponding instruction at that address. Code can also be written, e.g., self-modifying code DATAPATH Next, we have the program counter or PC. The PC is a state element that holds the address of the current instruction. Essentially, it is just a 32-bit register which holds the instruction address and is updated at the end of every clock cycle. Normally PC increments sequentially except for branch instructions The arrows on either side indicate that the PC state element is both readable and writeable. DATAPATH Lastly, we have the adder. The adder is responsible for incrementing the PC to hold the address of the next instruction. -
Effectiveness of the MAX-2 Multimedia Extensions for PA-RISC 2.0 Processors
Effectiveness of the MAX-2 Multimedia Extensions for PA-RISC 2.0 Processors Ruby Lee Hewlett-Packard Company HotChips IX Stanford, CA, August 24-26,1997 Outline Introduction PA-RISC MAX-2 features and examples Mix Permute Multiply with Shift&Add Conditionals with Saturation Arith (e.g., Absolute Values) Performance Comparison with / without MAX-2 General-Purpose Workloads will include Increasing Amounts of Media Processing MM a b a b 2 1 2 1 b c b c functionality 5 2 5 2 A B C D 1 2 22 2 2 33 3 4 55 59 A B C D 1 2 A B C D 22 1 2 22 2 2 2 2 33 33 3 4 55 59 3 4 55 59 Distributed Multimedia Real-time Information Access Communications Tool Tool Computation Tool time 1980 1990 2000 Multimedia Extensions for General-Purpose Processors MAX-1 for HP PA-RISC (product Jan '94) VIS for Sun Sparc (H2 '95) MAX-2 for HP PA-RISC (product Mar '96) MMX for Intel x86 (chips Jan '97) MDMX for SGI MIPS-V (tbd) MVI for DEC Alpha (tbd) Ideally, different media streams map onto both the integer and floating-point datapaths of microprocessors images GR: GR: 32x32 video 32x64 ALU SMU FP: graphics FP:16x64 Mem 32x64 audio FMAC PA-RISC 2.0 Processor Datapath Subword Parallelism in a General-Purpose Processor with Multimedia Extensions General Regs. y5 y6 y7 y8 x5 x6 x7 x8 x1 x2 x3 x4 y1 y2 y3 y4 Partitionable Partitionable 64-bit ALU 64-bit ALU 8 ops / cycle Subword Parallel MAX-2 Instructions in PA-RISC 2.0 Parallel Add (modulo or saturation) Parallel Subtract (modulo or saturation) Parallel Shift Right (1,2 or 3 bits) and Add Parallel Shift Left (1,2 or 3 bits) and Add Parallel Average Parallel Shift Right (n bits) Parallel Shift Left (n bits) Mix Permute MAX-2 Leverages Existing Processing Resources FP: INTEGER FLOAT GR: 16x64 General Regs. -
Chapter 6 - Combinational Logic Systems GCSE Electronics – Component 1: Discovering Electronics
Chapter 6 - Combinational logic systems GCSE Electronics – Component 1: Discovering Electronics Combinational logic systems Learners should be able to: (a) recognise 1/0 as two-state logic levels (b) identify and use NOT gates and 2-input AND, OR, NAND and NOR gates, singly and in combination (c) produce a suitable truth table from a given system specification and for a given logic circuit (d) use truth tables to analyse a system of gates (e) use Boolean algebra to represent the output of truth tables or logic gates and use the basic Boolean identities A.B = A+B and A+B = A.B (f) design processing systems consisting of logic gates to solve problems (g) simplify logic circuits using NAND gate redundancy (h) analyse and design systems from a given truth table to solve a given problem (i) use data sheets to select a logic IC for given applications and to identify pin connections (j) design and use switches and pull-up or pull-down resistors to provide correct logic level/edge-triggered signals for logic gates and timing circuits 180 © WJEC 2017 Chapter 6 - Combinational logic systems GCSE Electronics – Component 1: Discovering Electronics Introduction In this chapter we will be concentrating on the basics of digital logic circuits which will then be extended in Component 2. We should start by ensuring that you understand the difference between a digital signal and an analogue signal. An analogue signal Voltage (V) Max This is a signal that can have any value between the zero and maximum of the power supply. Changes between values can occur slowly or rapidly depending on the system involved. -
CS 61C: Great Ideas in Computer Architecture Combinational and Sequential Logic, Boolean Algebra
CS 61C: Great Ideas in Computer Architecture Combinational and Sequential Logic, Boolean Algebra Instructor: Justin Hsia 7/24/2013 Summer 2013 ‐‐ Lecture #18 1 Review of Last Lecture • OpenMP as simple parallel extension to C – During parallel fork, be aware of which variables should be shared vs. private among threads – Work‐sharing accomplished with for/sections – Synchronization accomplished with critical/atomic/reduction • Hardware is made up of transistors and wires – Transistors are voltage‐controlled switches – Building blocks of all higher‐level blocks 7/24/2013 Summer 2013 ‐‐ Lecture #18 2 Great Idea #1: Levels of Representation/Interpretation temp = v[k]; Higher‐Level Language v[k] = v[k+1]; Program (e.g. C) v[k+1] = temp; Compiler lw $t0, 0($2) Assembly Language lw $t1, 4($2) Program (e.g. MIPS) sw $t1, 0($2) sw $t0, 4($2) Assembler 0000 1001 1100 0110 1010 1111 0101 1000 Machine Language 1010 1111 0101 1000 0000 1001 1100 0110 Program (MIPS) 1100 0110 1010 1111 0101 1000 0000 1001 0101 1000 0000 1001 1100 0110 1010 1111 Machine Interpretation We are here Hardware Architecture Description (e.g. block diagrams) Architecture Implementation Logic Circuit Description (Circuit Schematic Diagrams) 7/24/2013 Summer 2013 ‐‐ Lecture #18 3 Synchronous Digital Systems Hardware of a processor, such as the MIPS, is an example of a Synchronous Digital System Synchronous: •All operations coordinated by a central clock ‒ “Heartbeat” of the system! Digital: • Represent all values with two discrete values •Electrical signals are treated as 1’s -
Avocado: a Secure In-Memory Distributed Storage System
Avocado: A Secure In-Memory Distributed Storage System Maurice Bailleu , Dimitra Giantsidi Vasilis Gavrielatos , Do Le Quoc , Vijay Nagarajan , Pramod Bhatotia University of Edinburgh 1Huawei Research 1 TU Munich 1 2∗ 1 1,3 1 2 3 Abstract hypervisor. Given this promise, TEEs are now commercially oered by major cloud computing providers [23, 34, 60]. We introduce Avocado, a secure in-memory distributed Although TEEs provide a promising building block for se- storage system that provides strong security, fault-tolerance, curing systems againsta powerfuladversary,theyalso present consistency (linearizability) and performance for untrusted signicant challenges while designing a replicated secure cloud environments. Avocado achieves these properties distributed storage system. The fundamental issue is that the based on TEEs, which, however, are primarily designed TEEs are primarily designed to secure the limited in-memory for securing limited physical memory (enclave) within a state of a single-node system, and thus, the security properties single-node system. Avocado overcomes this limitation by of TEEs do not naturally extend to a distributed infrastructure. extending the trust of a secure single-node enclave to the Therefore we ask the question: How can we leverage TEEs distributed environment over an untrusted network, while to design a high-performance, secure, and fault-tolerant ensuring that replicas are kept consistent and fault-tolerant in-memory distributed KVS for untrusted cloud environments? in a malicious environment. To achieve these goals, we design and implement Avocado In this workwe introduce Avocado,a secure,distributedin- underpinning on the cross-layer contributions involving the memory KVS based on Intel SGX [5] as the foundational TEE security network stack, the replication protocol, scalable trust estab- that achieves the following properties: (a) strong , in condentiality lishment, and memory management.