Announcements. This week: no lab, no quiz, just midterm

Transcription

1 CSC258 Week 7

2 Announcements This week: no lab, no quiz, just midterm 2

3 Recap ALU Multiplication 3

4 To implement multiplication, we basically repeatedly do three things AND (one-bit multiplication) Addition Shift How to do shift? 4

5 Example: Barrel Shifter D3 D2 D D0 S0 S S S S S S S S S 0 4-to- MUX 4-to- MUX 4-to- MUX 4-to- MUX Y3 Y2 Y Shift data elements according to S 0 and S. Y0 If SS0 = 00: Y3Y2YY0 = D3D2DD0 If SS0 = 0: Y3Y2YY0 = D2DD0D3 5

6 Make multiplication more efficient Think about 258 x 9999 Multiply by 9, add to sum, shift, multiply by 9, add to sum, shift, multiple by 9, add to sum, shift, multiply by 9, add to sum. 258 x 9999 = 258 x ( ) = 258 x Just shift 258, becomes , then do More efficient! 6

7 More efficient multiplication: Booth s Algorithm Take advantage of circuits where shifting is cheaper than adding, or where space is at a premium. ú when multiplying by certain values (e.g. 99), it can be easier to think of this operation as a difference between two products. Consider the shortcut method when multiplying a given decimal value X by 9999: ú X*9999 = X*0000 X* Now consider the equivalent problem in binary: ú X*00 = X*00000 X* More details: 7

8 Reflections on multiplication Multiplication isn t as common an operation as addition or subtraction, but occurs enough that its implementation is handled in the hardware. Most common multiplication and division operations are powers of 2. For this, the shift register is used instead of the multiplier circuit. ú e.g., in your code, do x << 3, instead of x * 8 8

9 Recap: We are here Assembly Language Processors Arithmetic Logic Units Devices Finite State Machines Flip-flops Circuits Gates Transistors 9

10 Next Controller Thing Storage Thing Arithmetic Thing 0

11 The Blueprint of a microprocessor The Controller Thing PCWriteCond PCWrite IorD MemRead MemWrite MemtoReg IRWrite Contr ol Unit Opcode PCSource ALUOp ALUSrcB ALUSrcA RegWrite RegDst Shift left PC 0 Address Write data Memor y Memory data Instruction [3-26] Instruction [25-2] Instruction [20-6] Instruction [5-0] Instructi on Register Memory data register 0 0 Register s Read reg Read Read reg 2data Write reg Write data Sign extend Read data 2 A B Shift left A B Zero ALU result AL U ALU Out The Storage Thing The Arithmetic Thing

12 We ve learned the arithmetic thing ALU C in,s A B VCNZ With ALU, we can do addition, subtraction, logic operations, etc. G 2

13 So this is the ALU A B C in,s VCNZ G So where do A and B come from? 3

14 The Storage Thing aka: the register file and main memory 4

15 Computer memory hierarchy Sorted by data (food) access speed Register: that plate in front of you Cache: the fridge in the kitchen Memory: the grocery store downstairs Hard disk: the farm in the suburb Network: the farm in a different country 5

16 Memory and registers There are units in the CPU that store multiple data values for use by the CPU: ú Registers: Small number of fast memory units that allow multiple values to be read and written simultaneously. ú Main memory: Larger grid of memory cells that are used to store the main information to be processed by the CPU. 6

17 Registers are in here Memory is in here 7

18 Registers are in here in the CPU Memory chips are plugged in here 8

19 9

20 Register file An array of registers in the CPU 20

21 Register File Functionality Read/Write Destination Reg. (n-bit address) Data to write Register A (n-bit address) Register B (n-bit address) Register 0 Register Register 2 Register File Register 2 n Register File Typical setup (MIPS): Each register is 32-bit There are 32 registers. 5-bit address Value from Reg. A Value from Reg. B 2

22 Register File Write Operation Data Load Enable Load Load R 0 R A select A Load Load R 2 R B Decoder B select D address 22

23 Register File Read Operation Data Load Enable Load Load R 0 R A select A Load Load R 2 R B Decoder B select D address 23

24 The main memory An array of memory units 24

25 Electronic Memory Like register files, main memory is made up of a decoder and rows of memory units. Address Lines m Decoder Row 0 Row Row 2 Row 3... Row 2 m - These lines are used for both input and output (called bus)... D 0 D D 2 D n- Data Lines 25

26 One-hot decoder The decoder takes in the m-bit binary address, and activates a single row in the memory array. A 2 A A 0 O 7 O 6 O 5 O 4 O 3 O 2 O O

27 Controlling the flow Since some lines (buses) will now be used for both input and output, we introduce a (sort of) new gate called the tri-state buffer. A WE Y When WE (write enable) signal is low, buffer output is a high impedance signal. WE A Y 0 X Z 0 0 ú The output is neither connected to high voltage or to the ground. 27

28 WE WE A Y A WE = Y 0 X Z 0 0 A Y WE = 0 A Y 28

29 Control the flow using tri-state buffer Control c0, c and c2 so that only one of the devices output is written to the bus. In general, the bus can be read by multiple devices at the same but can only be written by one device at a time. 29

30 Data Bus Communication between components takes place through groups of wires called a bus (or data bus). ú Multiple components can read from a bus, but only one can write to a bus at a time. Also called a bus driver. ú Each component has a tri-state buffer that feeds into the bus. When not reading or writing, the tri-state buffer drives high impedance onto the bus. 30

31 RAM Storage Cell what stores each bit of the memory 3

32 Storage cells For storing a single bit Each row is made of an array of storage cells. Multiple ways of representing these cells. ú e.g. RAM cell (basically a gated latch) Select B S Q C B R Q RAM cell C 32

33 RAM slice model Word select signals (via a one-hot decoder) determine which row to send out on the C lines. Word select 0 Word select 2 n - B B Select Select S R S R Q Q Q Q RAM cell RAM cell C X X C X X Word select 0 Word select Word select 2 n 2 RAM cell RAM cell RAM cell Read/Write logic Data in Data out Read/ Bit Write select (b) Symbol Data in S R Q Q Read/ Write Write logic Bit select Read logic Data out 33

34 RAM slice model Or, use word select to choose row, and use bit select to choose column. 34

35 Example: SRAM Static Random Access Memory There are other types of RAMs such as DRAM, SDRAM, DDR SDRAM, RDRAM, VRAM, etc. 35

36 Asynchronous SRAM Interface An example Address (n-bit) CE Read/Write OE SRAM Data (m-bit) Chip Enable (CE ) Read/Write Output Enable (OE ) Access Type 0 0 X SRAM Write 0 0 SRAM Read X X SRAM not enabled 36

37 Read/Write SRAM - Timing waveforms Clock SRAM Read SRAM Write Address CE Read/ Write OE Data hi-z hi-z hi-z Data from SRAM Data to SRAM Reading and writing of signals takes time. To make sure things are read/written correctly, we must control the timing carefully. 37

38 Memory vs registers Memory houses most of the data values being used by a program. Registers are more local data stores, meant to be used to execute an instruction. ú Registers are not meant to host memory between instructions (like scrap paper for a calculation). ú Exception is the stack pointer register, which is sometimes in the same register file as the others. 38

39 Next The Controller Thing PCWriteCond PCWrite IorD MemRead MemWrite MemtoReg IRWrite Contr ol Unit Opcode PCSource ALUOp ALUSrcB ALUSrcA RegWrite RegDst Shift left PC 0 Address Write data Memor y Memory data Instruction [3-26] Instruction [25-2] Instruction [20-6] Instruction [5-0] Instructi on Register Memory data register 0 0 Register s Read reg Read Read reg 2data Write reg Write data Sign extend Read data 2 A B Shift left A B Zero ALU result AL U ALU Out 39