ALUs and Data Paths. Subtitle: How to design the data path of a processor. 1/8/ L3 Data Path Design Copyright Joanne DeGroat, ECE, OSU 1

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1 ALUs and Data Paths Subtitle: How to design the data path of a processor. Copyright Joanne DeGroat, ECE, OSU 1

2 Lecture overview General Data Path of a multifunction ALU Copyright Joanne DeGroat, ECE, OSU 2

3 of ALUs and Data Paths Objective: a General Purpose Data Path such as the datapath found in a typical computer. A Data Path Contains: Registers general purpose, special purpose Execution Units capable of multiple functions Copyright Joanne DeGroat, ECE, OSU 3

4 ALU Operations Add (A+B) Add with (A+B+n) Subtract (A-B) Subtract with Borrow (A-B-n) [Subract reverse (B-A)] [Subract reverse with Borrow (B-A-n)] Negative A (-A) Negative B (-B) Increment A (A+1) Increment B (B+1) Decrement A (A-1) Decrement B (B-1) Logical AND Logical OR Logical XOR Not A Not B A B Multiply Step or Multiply Divide Step or Divide Mask Conditional AND/OR (uses Mask) Shift Zero Copyright Joanne DeGroat, ECE, OSU 4

5 A High Level Copyright Joanne DeGroat, ECE, OSU 5

6 The AMD 2901 Bit Slice ALU Copyright Joanne DeGroat, ECE, OSU 6

7 The Architecture Copyright Joanne DeGroat, ECE, OSU 7

8 Arithmetic Logic rcuits The Brute Force Approach A more modern approach Copyright Joanne DeGroat, ECE, OSU 8

9 Arithmetic Logic rcuits The Brute Force Approach AB AB A B A Cout A FA B n Function N to 1 Mux A more modern approach Copyright Joanne DeGroat, ECE, OSU 9

10 Arithmetic Logic rcuits The Brute Force Approach AB AB A B A Cout A FA B n Function N to 1 Mux A B A B A more modern approach S Logic Unit 2 to 1 Mux Arithmetic Unit Copyright Joanne DeGroat, ECE, OSU 10

11 A Generic Function Unit Desire a generic functional unit that can perform many functions A 4-to-1 mux will perform all basic logic functions of 2 inputs Copyright Joanne DeGroat, ECE, OSU 11

12 Low level implementation At the implementation Level the design can be With transmission gates Very important for VLSI implementation Implementation has a total Of 16 transistors. Copyright Joanne DeGroat, ECE, OSU 12

13 Low level implementation An implementation in pass gates (CMOS) When the control signal is a 1 the value will be transmitted Otherwise it is an open switch A B A B G(A,B) AB A+B AxorB G G G G Copyright Joanne DeGroat, ECE, OSU 13

14 Lets look at Binary Addition We can use this generic function unit construct a generic ALU. For Binary Addition consider the following: SUMi = Ai xor Bi xor +1 = + Ai + Bi A B n Sum Cout Copyright Joanne DeGroat, ECE, OSU 14

15 An Alternative - Define two signals Equations for P and K = Ai xor Bi = A B Now can reform equations into functions of P and K Copyright Joanne DeGroat, ECE, OSU 15

16 New functions Using these definitions of P and K SUMi = xor +1 = + = + AB You can use the generic functional blocks to generate P and K and then select the correct function for final output Copyright Joanne DeGroat, ECE, OSU 16

17 A bit slice of the ALU Slice starts out with a generic unit which can produce any function of inputs Ai and Bi to produce P Need another to produce K And a 3 rd to generate the result And also need a dedicated unit to compute the carry out, the +1 term +1 ll Copyright Joanne DeGroat, ECE, OSU 17

18 Generation of the carry out The carry chain is the critical path for arithmetic operations. A simple ripple carry circuit is shown here for the slice Actual implementation depend on the technology in which implemented. Copyright Joanne DeGroat, ECE, OSU 18

19 chain implementation CMOS Manchester carry chain using precharge pulldown logic works well. ECL look-ahead circuitry works well as ECL allows for large fan-in wired OR gates. Copyright Joanne DeGroat, ECE, OSU 19

20 Multibit implementation ll ll ll ll ll ll ll ll Copyright Joanne DeGroat, ECE, OSU 20

21 Function codes 0 NOR A B A AB B XOR A B A B G G G G G NAND AND XNOR B A +B A A+B OR 1 The G values for the various logic functions By setting the value of the G inputs the output is the Corresponding logic function of the data which comes in On the select inputs. Copyright Joanne DeGroat, ECE, OSU 21

22 Binary Subtraction Much like addition but now choose P = A xnor B K = A B Diff D = A xor B xor Bin = A xnor B xnor Bin Borrow Out Bout=P Bin + P K P K A B Bin Diff Bout Copyright Joanne DeGroat, ECE, OSU 22

23 The codes to have the ALU work Consider as we go to the sliced ALU Logic function done in the P generic unit Math used all the blocks Function P K R n A A and B OR A + B + n n A+B Incr A A B or Bin Copyright Joanne DeGroat, ECE, OSU 23

24 Multibit implementation ll ll ll ll ll ll ll ll Copyright Joanne DeGroat, ECE, OSU 24