ECE 331 Hardware Organization and Design. UMass ECE Discussion 11 4/12/2018

Transcription

1 ECE 331 Hardware Organization and Design UMass ECE Discussion 11 4/12/2018

2 Today s Discussion Topics Hamming Codes For error detection and correction Virtual Machines Virtual Memory

3 The Hamming SEC Code Hamming distance Number of bits that are different between two bit patterns binary string # binary string #2 This leads to a Hamming distance of 2 Minimum distance = 2 provides single bit error detection e.g. parity code Minimum distance = 3 provides single error correction, 2 bit error detection ECE232: Introduction to Virtual Memory 16

4 Encoding SEC (Single Error Correcting) To calculate Hamming code: Number bits from 1 on the left All bit positions that are a power 2 are parity bits Each parity bit checks certain data bits: Note: In a break from convention, we start numbering bits from 1 on the left (MSB), as opposed to the rightmost (LSB) bit being zero ECE232: Introduction to Virtual Memory 17

5 Decoding SEC Value of parity bits indicates which bits are in error Use numbering from encoding procedure Example: We have an 8 bit value: Add 4 bits for parity checking: 1_001 _1010 Bit 1 Bit 2 Bit 4 Bit 8 Bit 1 (0001) covers all bit locations that have a 1 in the LSB (e.g. 0001, 0011, etc., but not 0010, 0110, etc.) Bit 2 (0010) covers all bit locations that have a 1 in the 2 nd bit (e.g. 0010, 0011, etc., but not 0001, 0101, etc.) Bit 4 (0100) covers all bit locations that have a 1 in the 3 rd bit (e.g. 0100, 0101, etc., but not 0001, 1011, etc.) ECE232: Introduction to Virtual Memory 18

6 Example continued Fill out the remaining parity bits based on the rules of parity. In this case, for even parity 1_001 _1010 Bit 1 Bit 2 Bit 4 Bit 8 Bit 1: (add bits 1, 3, 5, 7, 9, and 11) à Bit 1 = 0 Bit 2: (add bits 2, 3, 6, 7, 10, and 11) à Bit 2 = 1 Bit 4: (add bits 4, 5, 6, 7, and 12) à Bit 4 = 1 Bit 8: (add bits 8, 9, 10, 11, and 12) à Bit 8 = 0 The resulting 12-bit value, that includes the Hamming correction code is ECE232: Introduction to Virtual Memory 19

7 Example continued If there is a single bit-error in the data stored in memory, we have We can check the parity bits Bit 1: add bits 1, 3, 5, 7, 9, and 11 = 4, even, okay! Bit 2: add bits 2, 3, 6, 7, 10, and 11 = 5, odd, error! Bit 4: add bits 4, 5, 6, 7, and 12 = 2, even, okay! Bit 8: add bits 8, 9, 10, 11, and 12 = 3, odd, error! Add the bit locations together to find out where the error is: = 10. An error in Bit 10 Flip bit 10, 1 à 0 This fixes the problem! As long as there is only one error, this works for all bits, including the parity bits. ECE232: Introduction to Virtual Memory 20

8 An example Received data on even parity channel: 0xAC3 Is there an error? If so, where? What is the original data?

9 SEC/DEC SEC/DED Code Add an additional parity bit for the whole word (p n ) Make Hamming distance = 4 Decoding: Let H = SEC parity bits H even, p n even, no error H odd, p n odd, correctable single bit error H even, p n odd, error in p n bit H odd, p n even, double error occurred Note: ECC DRAM uses SEC/DEC with 8 bits protecting every 64 bits. With 72 bits, we can have Single Bit Error Corrections and Double Error Detections. Many DIMMS are 72 bits wide. SEC/DED Can be done across memory systems (e.g. hard drives for RAID) ECE232: Introduction to Virtual Memory 21

10 Virtual Machines Host computer emulates guest operating system and machine resources Improved isolation of multiple guests Avoids security and reliability problems Aids sharing of resources Virtualization has some performance impact Feasible with modern high-performance comptuers Examples IBM VM/370 (1970s technology!) VMWare Microsoft Virtual PC ECE232: Introduction to Virtual Memory 3

11 Virtual Machine Monitor (VMM) Maps virtual resources to physical resources Memory, I/O devices, CPUs Guest code runs on native machine in user mode Traps to VMM on privileged instructions and access to protected resources Guest OS may be different from host OS VMM handles real I/O devices Emulates generic virtual I/O devices for guest Guest OS s: VM1 VM2 VM3 Host OS VMM I/O Processor, running ISA ECE232: Introduction to Virtual Memory 23

12 Virtual Memory - Objectives 1. Allow program to be written without memory constraints program can exceed the size of the main memory 2. Many Programs sharing DRAM Memory so that context switches can occur 3. Relocation: Parts of the program can be placed at different locations in the memory instead of a big chunk Virtual Memory: I. Main Memory holds many programs running at same time (processes) II. use Main Memory as a kind of cache for disk Datapath Processor Control Cache Regs Main Memory (DRAM) Disk ECE232: Introduction to Virtual Memory 7

13 Two Tasks sharing the Physical Memory ECE232: Introduction to Virtual Memory 11