CS 2630 Computer Organization. Meeting 13: Faster arithmetic and more operations Brandon Myers University of Iowa
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1 CS 2630 Computer Organization Meeting 13: Faster arithmetic and more operations Brandon Myers University of Iowa
2 Where we are going Compiler Instruction set architecture (e.g., MIPS) translating source code (C or Java) Programs to assembly language And linking your code to Library code How the software talks To the hardware Memory system Processor Datapath & Control Digital logic I/O system How a processor runs MIPS Programs! How switches (1 or 0) can be used to build Interesting functions: from integer arithmetic to programmable computers
3 Ingredients for a processor Combinational logic arithmetic and bitwise operations multiplexors (pick 1 out of of N inputs) control logic branch calculation address calculation start learning how to build these combinational logic circuits Synchronous logic (we ll get to these later) registers program counter, or PC data memory instruction memory
4 How do we add two numbers addu $t0, $t1, $t2 We know: The numbers are physically stored in registers as bits The sum of two numbers is a function we can implement using combinational logic
5 Delay of adder circuit 1-bit adder delay: sum=2 1-bit adder delay: carry=1 0 A0 B0 A1 B1 A2 B2 A31 B Sum0 Sum1 Sum2 Sum31 This adder is called ripple carry adder
6 Carry-select adder
7 Peer instruction 1 time signal is available shown in red/bold delays: sum: 1 carry: 1 mux: What is the delay from the time A and B are available to when Sum is available? 2
8 Administrivia Review session last night (get notes from peers if you were not there) No DYB today Midterm this Thursday, 10/6, in class open notes / open textbook (recommend making a single sheet of important information rather than flipping through book) no electronics allowed
9 Best case delay of adders? O(log n) compute carries p means propagate a carry g means generate a carry use carries to finish the sums important: p and g are not functions of c
10 Best case delay of adders? O(log n) compute carries critical path use carrys to finish the sums
11 Shifting by a constant
12 Variable shifter: first attempt with 1-bit muxes
13 Variable shifter, similar design with 8-bit mux hardwired shifts by each possible shift amount Can you think of a design that avoids using a huge 8-bit x 8-choice mux? e.g., using only 8-bit x 2-choice muxes and hardwired shifters? pick which one using the shift amount
14 Multi-stage shifter using the magic of binary decision-making Hint: Recall the envelopes from HW1 another solution (but uses more 2-input MUXs) is to build the 8-input MUX on the previous slide using 2-input MUXs, like a soccer tournament with 8 teams and one champion
15 Multiplication Evaluate x on paper Evaluate x on paper
16 Peer instruction Build a 2-bit multiplier (4-bit output) you may use any number of example test cases: 01 * 01 = * 01 = * 11 = * 11 = 1001
17 Ingredients for a processor Combinational logic arithmetic and bitwise operations multiplexors (pick 1 out of of N inputs) control logic branch calculation address calculation Synchronous logic registers program counter, or PC data memory instruction memory
18
19 Basic memory element: flip-flop clock pulse rising edge value to store D Q stored value on the rising edge of the clock signal, the value on input D is captured into the flip-flop value of the output Q is the value stored in the flip-flop
20 Clock signal Analogy with a clock on the wall: every tick happens instantaneously at the rising edge the period is the time between ticks period of a wall clock: 1 second period of a typical digital logic clock: nanoseconds or less
21 Peer instruction D Q 0 NAND 1 T0 T1 T2 Q 0 1 0??? What is the value of Q after T0, after T1, and after T2? (enter three numbers: 0 or 1, 0 or 1, 0 or 1)
22 Next steps use 32 flip-flops in parallel to create 32-bit registers for our MIPS processor learn about Finite State Machines, a way of thinking about circuits with flip-flops and combinational logic arrange stored bits into large memories and learn how to lookup values using an address
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