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Chapter 5. Control Design
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* Two approaches for control unit design
• A hard-wired control unit : a sequential logic circuit to generate specific fixed sequences of control signals → change in behavior only by redesign. 5.5
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• A microprogrammed control unit
: by organizing control signals into microinstructions. The signals are implemented by a kind of software(or firmware) rather than hardware. → design change : change the contents of control memory. → emulation : a microprogrammed CPU can execute programs written in the machine language of other computers. Disadvantage: ① Slower due to fetch. ② more costly due to the presence of the control memory and its access circuits.
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Hardwired Control design method 1 : The classical method of sequential circuit design. For a P-state circuit, log2P flip-flops are required. design method 2 : One-hot method, one flip-flop per state. Expensive in terms of F/F but simplify CU design and debugging. • GCD processor
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Classical method S0 = 00, S1 = 01, S2 = 10 and S3 = 11
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(5.9) (5.10) (5.11)
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One-hot method S0 = 0001, S1 = 0010, S2 = 0100 and S3 = 1000
The one-hot method is limited to a small number of states The next-state and output equations have a simple and systematic form The one-hot design method 1. Construct a P-row state table that defines the desired input-output behavior. 2. Associate a separate D-type flip-flop Di with each state Si, and assign the P-bit one-hot binary code D1, D2 , … , Di-1, Di , Di+1 , … , Dp = 0,0,…,0,1,0,…,0 to Si. 3. Design a combinational circuit C that generates the primary and secondary output signals { Di } and { zk }, respectively. Di+ is defined by the logic equation where denote all input combinations that cause a transition from Sj to Si. If zk = 1 ( active ) only in rows k,h for h = 1,2,…,mk, then zk is defined by
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Design of 2C multiplier hardwired control
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5.2 Microprogrammed Control
Instruction : implemented by a sequence of one or more sets of concurrent micro-operations. Microprogramming : control-signal selection and sequencing information is stored in a ROM or RAM called a control memory(CM), and microinstruction is fetched from CM. A microprogrammed computer C1 can be used to execute program written in the machine language L2 of some other computer C2 by placing an emulation for L2 in the CM of C1.
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Wilker’s Design : microinstruction (I)
Control field Address field Wilker’s Design : microinstruction (I)
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How to decide I word length
1. The degree of parallelism required at the micro-operation level 2. How the control information is represented or encoded 3. How to specify the next I address Parallelism in I If all useful combination of parallel micro-operation are specified by a single opcode it would be enormous, and decoder will be complicated. → divide the micro-operation specification part into k disjoint control field, any one of which can be performed simultaneously with other. ① In IBM 360/50: I 90 bits (21 partitioned control field) ② Wilker design: 1-bit control field for each control signal. Un-encoded form (4-bit) X0 ○ c0 X1 c1 X2 c2 X3 c3 Register R c0 c1 c2 c3 Micro-operation R← X0 R← X1 R← X2 R← X3 No op
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Encoded form (3-bit) Micro-operation 5 operations
K0 K1 K2 Micro-operation R← X0 R← X1 R← X2 R← X3 No op 5 operations n independent control signal → ⌈log2(n+1)⌉ bits decoder is needed I : horizontal VS vertical horizontal form : ① long format ② able to express a high degree of parallelism ③ little encoding for the control information. vertical form : ① short format ② limited ability to express parallelism ③ considerable encoding of the control information.
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I addressing – use PC (as the primary source) – conditional branching Condition select subfield branch address : store a complete address field or lower-order bits of address. restricting the range of branch instruction to a small region of CM Timing – monophase : a simple clock pulse synchronize all the control signals. control signals are active for the duration of instruction’s execution cycle – polyphase : divide a clock cycle into phases and control signal is active during one of the phase Increase the complexity of the I format ( to specify the phase of which control signal)
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Ex) Timing of 4-phase I. ( R ← R1 op R2 )
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A microprogram sequencer generates
a I addresses for CM and comprises PC and all the logics needed for next address generation
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Minimizing the width of CM
Is: I1, I2, ···, In Each activates a subset of control signals C1, C2, ··· , Cm ⇒ want an encoding method CM width length Control field decoder 1 decoder 2 decoder 3 ··· ci ck cj control field ⇒ achieve the minimum number of bits in the control field maintaining the parallelism can’t be activated at the same time. An encoded control field can activate only one control signal at a time. Two control signals can be included in the same control field if and only if they are never simultaneously activated by a I.
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1. Every control signal is contained in at least one {Ci}.
• The minimization problem: Find a set of compatibility class {Ci} such that 1. Every control signal is contained in at least one {Ci}. 2. The width W = ∑ log2( |Ci| + 1 ) is minimized. i Algorithm 1. Find the set of Maximal compatibility class (MCC), defined as the compatibility classes to which no control signal can be added without introducing a pair of incompatible control signals. An encoded control field can activate only one control signal at a time. Two control signals can be included in the same control field iff they are never simultaneously activated by a I. (i.e. they are compatible). Two control signals Ci1 and Ci2 are compatible if Ci1Ij implies Ci2Ij, and vice versa. The compatibility class is a set of control signals that are pairwise compatible. 2. Determine all minimal MCC covers. A minimal MCC cover is the minimal set of MCC that includes each control signal. ( Note that a minimal MCC cover does not always yield a minimum value of the cost function W ). 3. For each minimal MCC covers, include each control signal in exactly one subset of some {Ci} and execute the cost W of the resulting solutions and select one with the minimal cost.
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Deriving MCC : Denote Si as the set of compatibility classes {Ci} such that {Ci} contains i Cij control signals. S1={simply the n original control signals} Si forms all possible(i)- member compatibility classes. Using Si, construct Si+1 as follow; For each {Ci}Si, add a control signal Cik to {Ci} to form {C}. If {C} is a compatibility class, then add {C} to Si+1 and delete {Ci} and all subset of {C} from Si . Stop when Sk= for some kn+1. The MCCs are from Example: Find the minimum # of bits in the control fields. I Control signal I a, b, c, g S1 = a, b, c, d, e, f, g, h I2 a, c, e, h S2 = bd, be, bh, cd, de, dg, ef, eg, fg, fh, gh, dh I a, d, f S3 = bde, bdh, deg, dgh, efg, fgh I4 b, c, f S4 =
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Minimal MCC covers (similar to the prime implicant covering problem)
Cover Table – row for each MCC Ci – column for each control signal Cij C1 = a, C2 = cd, C3 = bde, C4 = bdh, C5 = deg, C6 = dgh, C7 = efg, C8 = fgh a b c d e f g h C1=a C2=cd C3=bde C4=bdh C5=deg C6=dgh C7=efg C8=fgh If a control signal Cij is covered by only one MCC {Ci }, then {Ci } is an essential MCC. If MCC {Ci } contains an in every row where MCC {Ck } contains an , then {Ci} dominates {Ck}. If a control signal Cij has an in every column where a control signal Ckl has an , then Cij dominates Ckl.
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Find the Minimal MCC covers
Find the Minimal MCC covers Row and column deletion from a cover table Delete all essential MCC and all column with in essential rows Delete all but one of identical columns Delete all domination columns Delete all domination rows. After finding two essential MCC {C1} and {C2}, we can get the reduced cover table. b e f g h C3=bde C4=bdh C5=deg C6=dgh C7=efg C8=fgh If C1+C2+C3+C8, a b c d e f g h C1=a C2=cd C3=bde C8=fgh C5 covered by C7 and C6 is also covered by C8; therefore, C5 & C6 can be removed. Minimal covers {C1+C2} +{C3+C8} +{C4+C7}
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If {C1,C2,C3,C8}={a, c, bde, fgh}→ width W = 1+1+2+2 = 6 bits
⇒ d is covered two times If {C1,C2,C3,C8}={a, cd, be, fgh}→ width W = log2(|C|+1) = = 7 bits If {C1,C2,C3,C8}={a, c, bde, fgh}→ width W = = 6 bits Another minimal MCC covers C1+C2+C3+C8 a b c d e f g h C1=a C2=cd C4=bdh C7=efg Using {a, c, bde, fgh} 1 I4 I3 I2 I1 5 4 3 2 -Instruction Minimize width Control field bits code control signal No op a No op c , No op b d e , No op f g h If {C1,C2,C4,C7}={a, cd, bh, efg} → width W = 7 bits If {C1,C2,C4,C7}={a, c, bdh, efg} → width W = 6 bits
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Encoding by function A drawback of the minimum-width control field : functionally unrelated control signals are combined.
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Multiple -Instruction formats
Branch instructions which specify no control signals. action instructions with no branching capability. This approach is used at the instruction level. 0 0 Control fields Action -Instruction Formats Branch -Instruction Condition select Branch address if Q(7) = 0 if COUNT6 = 1 jump
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with the advance of VLSI.
-program sequencer : to place all the circuitry required to generate I addresses in a single IC with the advance of VLSI. – a general purpose building block for -programmed CU. – simplify CPU design.
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nanoprogrammed Computer
• Nanoprogrammed Computer -programmed Computer. Instruction PC Control signals CM IR nanoprogrammed Computer Instruction PC nPC CM IR nCM Control signals nIR Criteria ① Size of CM ② Speed reduction(programming needs fetch one time/nanoprogramming twice) – due to extra memory access and complex controller. ③ The advantage of nanoprogramming is the greater design flexibility
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Total size : HmWm+HnWn = S2
(Compare the size of CM) Size of control memory in nanoprogramming Wm CM: ⇒HmWm Hm nCM: ⇒HnWn Wm Hn Total size : HmWm+HnWn = S2 Size of comparable single-level CM Wm ⇒HmWm = S1 Hm Usually, Hm large Wm small Hn small Wn large (Many micro-instructions can use the same nano programmed control)
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size = Hm (log2Hm + N ) =S1
Big adv. of nanoprogramming “Design flexibility” 1-level CM log2Hm N Wm Hm address Control signal size = Hm (log2Hm + N ) =S1 Nanoprogramming log2Hm N Hn log2Hn CM nCM Hm Assuming no branching address address S2 = Hm (log2Hm + log2Hn) + Hn N Let, r = Hn/Hm = ratio of unique nano-control states to total # of -control states for all instructions Hn = r·Hm S2 = Hm (log2Hm + log2r·Hm) + r·Hm N = Hm ( 2· log2Hm +log2r + r·N )
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In this case, nanoprogramming is better than microprogramming
Example) For 68,000 Processor(N = 70, Hm = 650, r = 0.4), which approach is better? log2650 70 650 1-level CM design : S1 = 650 (log2650 + 70) = 52,000 Nanoprogramming S1 = 650 (log2650 + log2260 )+ 260 70 = 30,550 log2650 70 260 log2260 650 In this case, nanoprogramming is better than microprogramming
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5.3 Pipeline Control Performance measure: by throughput in MIPS Cycle per instruction(CPI) = where f is the pipeline’s clock frequency.
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Efficiency(utilization): Em =
Speedup T(m) : the execution time on an m-stage pipeline T(1) : the execution time on a non-pipelined processor S(m) = m × E(m) Em = S(m) =
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PCR = Performance/cost ratio : where f : pipeline’s clock frequency K : hardware cost Suppose the pipeline has m stages for SI. a : the delay of a non-pipelined processor for SI each stage of P : delay a/m and extra delay b due to the buffer resister hardware cost K = cm + d c : buffer-register cost per stage d : cost of the pipelines data processing logic
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To maximize PCR with respect to m,
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5.3.3 Superscalar Processing
Superscalar operation performs more than one instruction per cycle by fetching, decoding, and executing several instructions concurrently. A superscalar computer has a single CPU that attempts to exploit the parallelism that is implicit in computer programs, with multiple execution units.
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In Fig. 5.66, the superscalar design has a potential speedup of 10.
With K independent m-stage pipeline E-units speedup factors of a superscalar CPU: heavy demand on the instruction-fetch logic a large, fast instruction and data cache Important factors for PCU of a superscalar computer • Instruction types: A floating-point add instruction has to be issued to a floating add instruction has to be issued to a floating-point E-unit, not to an integer E-unit. • E-unit availability. • Data dependencies : To avoid conflicting use of register, data-dependency constraints among the operands must be satisfied. • Control dependencies : Reduce the impact of branch instructions on pipeline efficiency. • Program order : Instructions must eventually produce results in the order, even if the results may be computed out-of-order internally. read dynamic instruction scheduling and branch prediction.
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