18-447 Computer Architecture Lecture 6 : Multi Cycle and Microprogrammed Microarchitectures. 1) Summary of my Work you w
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18-447 Computer Architecture Lecture 6 : Multi Cycle and
Microprogrammed Microarchitectures.
1) Summary of my Work you writings to be fulfilled here
THE BEST WAY TO DESIGN AN AUTOMATIC CALCULATING MACHINE By M. V. Wilkes, M.A., Ph.D., F.R.A.S. I would like to begin by adding my congratulations to the many others which have been received by Professor Williams, Manchester University and Ferranti Ltd., on the construction of the machine which has just been inaugurated. In the face of this beautifully engineered machine, the title I have chosen for my opening remarks in this discussion may sound a little impertinent. But, as Dr. Kilburn remarked yesterday, the designer of an electronic calculating machine must continually take decisions, and he does not know when he takes them whether they are right or wrong. I might put it by saying that in a mathematical sense the solution to the problem of designing an electronic calculating machine is unstable. Two similar groups of engineers with similar back- grounds and assisted by similar groups of mathematicians will, if working independently, produce quite different machines. Moreover, the machines finally built will depend on the scale on which the projects are conducted, the experience and back- ground of the teams, and the state of technical developments at the time. The last item is important since new developments in electron tubes, or in non-linear devices of the germanium type, might well affect even so fundamental a decision as the choice between the serial or parallel modes of operation for the machine. It is desirable, therefore, to keep under review the considerations which underlie the design of calculating machines and to try to examine them in the light of general principles as well as of current technical developments. I am aware that in doing this one is in danger of saying things which are sufficiently obvious without being said, but I am in the fortunate position of having been asked to open a discussion rather than to give a paper. I shall not, therefore, attempt to present a logical thesis but shall allow myself to raise issues rather than settle them. I think that most people will agree that the first considera- tion for a designer at the present time is how he is to achieve the maximum degree of reliability in his machine. Amongst other things the reliability of the machine will depend on the following: (a) The amount of equipment it contains. (b) Its complexity. (c) The degree of repetition of units. By the complexity of a machine I mean the extent to which cross-connections between the various units obscure their logical inter-relation. A machine is easier to repair if it consists of a number of units connected together in a simple way without cross-connections between them; it is also easier to construct since different people can work on the different units without getting in each other's way. As regards repetition I think everyone would prefer to have in a particular part of the machine a group of five identical units rather than a group of five different units. Most people would prefer to have six identical units rather than five different units. How far one ought to be prepared to go in the direction of accepting a greater quantity of equipment in order to achieve repetition is a matter of opinion. The matter may be put as follows. Suppose that it is regarded as being equally desirable to have a particular part of the machine composed of a group of n different units, or composed of a group of kn identical units, all the units being of similar size. What is the value of k? My conjecture is that k>2. I should say that I am thinking of a machine which has about 10 groups of units and that is approximately equal to 10. The remarks I have just made are of general application. I will now try to be more specific. If one builds a parallel machine one has a good example, in the arithmetical unit, of a piece of equipment consisting of identical units repeated many times. Such an arithmetical unit is, however, much larger than that in a serial machine. On the other hand I think it is true to say that the control in a parallel machine is simpler than in a serial machine. I am using the word control here in a very general sense to include everything that does not apper- tain to the store proper (i.e., it includes the access circuits) or to the registers and adders in the arithmetical unit. That the control can be simpler in a parallel machine may I think be seen by comparing the waveforms which must be produced in order to effect the transfer of a number from one register to another in a serial synchronous machine and in a parallel asynchronous machine. These are the two extreme cases. In the case of a serial synchronous machine the waveform must rise at some critical moment relative to the clock and must fall at another critical moment, and its edges must be sharp. In a parallel asynchronous machine all that is needed is a single pulse whose time of occurrence, length, and shape are all non-critical (see Fig. 9). SERIAL SYNCHRONOUS nnnnnnnnnn PARALLEL ASYNCHRONOUS Fig. 9. The arithmetical unit of a parallel machine is often shown diagrammatically as in Fig. 10. ADDEND REGISTER ADDER ACCUMULATOR SHFT REGISTER Fig. 10. At the beginning of a multiplication the multiplier is placed in the right-hand half of the accumulator register. The right- hand half of the shift register may be dispensed with if shifting is done in two stages. Showing the right-hand half of the accumulator as a separate register we then have the diagram of Fig. 11.
We are thus led to think of an arithmetical unit composed of a number of standard units each containing four flip-flops (one belonging to each of four registers) together with an adder. Gates would be provided to make possible the transfer of numbers from one register to another, through the adder when necessary. These transfers would be effected by pulsing one or more of a set of wires emerging from the arithmetical unit. Fig. 11. It is also necessary to have registers in the control of a machine. These, with the names given to them respectively in the Manchester machine and in the E.D.S.A.C., are as follows: Register for holding the address of the next order due to be executed (control, or sequence control tank). Register holding order at present being executed (current instruction register, or order tank). Register for counting the number of steps in a multiplication or shifting operation (not needed with the fast multiplier on the Manchester machine, timing control tank in the E.D.S.A.C.). In addition the Manchester machine has a number of B registers. If one B register is considered to be sufficient the parallel machine we are considering can use the same unit (containing 4 flip-flops and 1 adder) for the control registers as for arith- metical registers. In this way an extreme degree of repetition can be achieved. It remains to consider the control proper, that is, the part of the machine which supplies the pulses for operating the gates associated with the anthmetical and control registers. The designer of this part of a machine usually proceeds in an ad hoc manner, drawing block diagrams until he sees an arrangement which satisfies his requirements and appears to be reasonably economical. I would like to suggest a way in which the control can be made systematic, and therefore less complex. Each operation called for by an order in the order code of the machine involves a sequence of steps which may include transfers from the store to control or arithmetical registers, or vice versa, and transfers from one register to another. Each of these steps is achieved by pulsing certain of the wires associated with the control and arithmetical registers, and I will refer to it as a 'micro-operation." Each true machine operation is thus made up of a sequence or "micro-programme of micro-operations. Fig. 12 shows the way in which pulses for performing the micro-operations may be generated. The timing pulse which initiates a micro-operation enters the decoding tree and is routed to one of the outputs according to the number set on the register R. It passes into the rectifier matrix A and gives rise to pulses on certain of the output wires of this matrix according to the arrangement of the rectifiers. These pulses operate the gates associated with the control and arithmetical registers, and cause the correct micro-operation to be per- formed. The pulse from the decoding tree also passes into matrix B and gives rise to pulses on certain of the output wires of this matrix. These pulses are conducted, via a short delay line, to the register R and cause the number set up on it to be changed. The result is that the next initiating pulse to enter the decoding tree will emerge from a different outlet and will consequently cause a different micro-operation to be per- formed. It will thus be seen that each row of rectifiers in matrix A corresponds to one of the micro-orders in the sequence required to perform a machine operation. The system as described would enable a fixed cycle of opera- tions only to be performed. Its utility can be greatly extended by making some of the micro-orders conditional in the sense that they are followed by one of two alternative micro-orders according to the state of the machine. This can be done by making the output of the decoding tree branch before it enters matrix B. The direction the pulse takes at the branch is controlled by the potential on a wire coming from another part of the machine; for example, it might come from the sign. flip-flop of the accumulator. The bottom row of matrix A in Fig. 12 corresponds to a conditional micro-order. The matrix A contains sequences of micro-orders for performing all the basic operations in the order code of the machine. All that is necessary to perform a particular opera- tion is that "micro-control" shall be switched to the first micro- order in the appropriate sequence. This is done by causing the function digits of the order to be set up on the first four or five flip-flops of the register R, zero being set on the others. MATRIX A DECODING TREE MATRIX TO GATES IN ARITHMETICAL UNIT, ETC. TIMING PULSE DELAY FROM SIGN FLIP-FLOP OF ACCUMULATOR Fig. 12. A control system designed in this way is certainly very logical in structure but two comments, slightly contradictory in their implications, might be made. In the first place it might be said that there is nothing very new about the arrangement since it makes use of flip-flops, gates, and mixing diodes which are the elements out of which any control is built. With this criticism I would agree. In fact, the controls of various machines now in existence or being constructed could no doubt be drawn in some way closely resembling
184 Fig. 12. The other objection is that the scheme appears to be rather extravagant in equipment. This I think is not true, particularly if some departures from the precise form of Fig. 12 are allowed. I think that by starting with a logical layout one is likely to arrive at a final arrangement which is both logical and economical. Moreover, one is able to see at each stage what one is sacrificing in the way of logical layout in order to achieve economy and vice versa. In order to get some idea of the number of micro-orders required I have constructed a micro-programme for a simple machine with the following orders: add, subtract, multiply (two orders, one for the multiplier, one for the multiplicand), right and left shift (any number of places), transfer from the accumulator to the store, conditional operation depending on the sign of the number in the accumulator, conditional opera- tion depending on the sign of the number in the B register (one B register is assumed), transfer from the store to the B register, input, and output. The micro-programme also provides for the preliminary extraction of the order from the store (Stage 1 in E.D.S.A.C. terminology). Only 40 micro-orders are required to perform all these operations. The considerations involved in drawing-up a micro-pro- gramme resemble those involved in drawing-up an ordinary programme. The final details of the control are thus settled by a systematic process instead of by the usual ad hoc procedures based on the use of block diagrams. Of course, sound engineer- ing would be necessary to produce designs for the decoding Part II tree and the matrices which could be used for any desired micro-programme by arranging the rectifiers suitably in the matrices. One important advantage of this method of design- ing the control is that the order code need not be decided on finally until a late stage in the construction of the machine; it would even be possible to change it after the machine had been put into operation simply by rewiring the matrices. If desired some of the micro-orders can be made conditional in their action as well as (or instead of) conditional as regards the switching of micro-control. This can be done by making the output of the decoding tree branch before it enters matrix A. I doubt if much economy can be achieved this way and if it is done to any extent the advantage that micro- programming resembles ordinary programming is lost. Other variants of the scheme as I have described it will no doubt occur to you. The matrices may be regarded as very high-speed stores holding fixed information. If they could be replaced by an erasable store to which information could be transferred from the main store of the machine when required we should have a machine with no fixed order code; the programmer would, in fact, be able to choose his order code to suit his own requirements and to change it during the course of the pro- gramme if he considered it desirable. Such a machine would have a number of fascinating possibilities but I doubt whether, in view of the amount of equipment it would doubtless involve, its construction could be justified.
Microprogrammed Microarchitectures.
1) Summary of my Work you writings to be fulfilled here
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We are thus led to think of an arithmetical unit composed of a number of standard units each containing four flip-flops (one belonging to each of four registers) together with an adder. Gates would be provided to make possible the transfer of numbers from one register to another, through the adder when necessary. These transfers would be effected by pulsing one or more of a set of wires emerging from the arithmetical unit. Fig. 11. It is also necessary to have registers in the control of a machine. These, with the names given to them respectively in the Manchester machine and in the E.D.S.A.C., are as follows: Register for holding the address of the next order due to be executed (control, or sequence control tank). Register holding order at present being executed (current instruction register, or order tank). Register for counting the number of steps in a multiplication or shifting operation (not needed with the fast multiplier on the Manchester machine, timing control tank in the E.D.S.A.C.). In addition the Manchester machine has a number of B registers. If one B register is considered to be sufficient the parallel machine we are considering can use the same unit (containing 4 flip-flops and 1 adder) for the control registers as for arith- metical registers. In this way an extreme degree of repetition can be achieved. It remains to consider the control proper, that is, the part of the machine which supplies the pulses for operating the gates associated with the anthmetical and control registers. The designer of this part of a machine usually proceeds in an ad hoc manner, drawing block diagrams until he sees an arrangement which satisfies his requirements and appears to be reasonably economical. I would like to suggest a way in which the control can be made systematic, and therefore less complex. Each operation called for by an order in the order code of the machine involves a sequence of steps which may include transfers from the store to control or arithmetical registers, or vice versa, and transfers from one register to another. Each of these steps is achieved by pulsing certain of the wires associated with the control and arithmetical registers, and I will refer to it as a 'micro-operation." Each true machine operation is thus made up of a sequence or "micro-programme of micro-operations. Fig. 12 shows the way in which pulses for performing the micro-operations may be generated. The timing pulse which initiates a micro-operation enters the decoding tree and is routed to one of the outputs according to the number set on the register R. It passes into the rectifier matrix A and gives rise to pulses on certain of the output wires of this matrix according to the arrangement of the rectifiers. These pulses operate the gates associated with the control and arithmetical registers, and cause the correct micro-operation to be per- formed. The pulse from the decoding tree also passes into matrix B and gives rise to pulses on certain of the output wires of this matrix. These pulses are conducted, via a short delay line, to the register R and cause the number set up on it to be changed. The result is that the next initiating pulse to enter the decoding tree will emerge from a different outlet and will consequently cause a different micro-operation to be per- formed. It will thus be seen that each row of rectifiers in matrix A corresponds to one of the micro-orders in the sequence required to perform a machine operation. The system as described would enable a fixed cycle of opera- tions only to be performed. Its utility can be greatly extended by making some of the micro-orders conditional in the sense that they are followed by one of two alternative micro-orders according to the state of the machine. This can be done by making the output of the decoding tree branch before it enters matrix B. The direction the pulse takes at the branch is controlled by the potential on a wire coming from another part of the machine; for example, it might come from the sign. flip-flop of the accumulator. The bottom row of matrix A in Fig. 12 corresponds to a conditional micro-order. The matrix A contains sequences of micro-orders for performing all the basic operations in the order code of the machine. All that is necessary to perform a particular opera- tion is that "micro-control" shall be switched to the first micro- order in the appropriate sequence. This is done by causing the function digits of the order to be set up on the first four or five flip-flops of the register R, zero being set on the others. MATRIX A DECODING TREE MATRIX TO GATES IN ARITHMETICAL UNIT, ETC. TIMING PULSE DELAY FROM SIGN FLIP-FLOP OF ACCUMULATOR Fig. 12. A control system designed in this way is certainly very logical in structure but two comments, slightly contradictory in their implications, might be made. In the first place it might be said that there is nothing very new about the arrangement since it makes use of flip-flops, gates, and mixing diodes which are the elements out of which any control is built. With this criticism I would agree. In fact, the controls of various machines now in existence or being constructed could no doubt be drawn in some way closely resembling
184 Fig. 12. The other objection is that the scheme appears to be rather extravagant in equipment. This I think is not true, particularly if some departures from the precise form of Fig. 12 are allowed. I think that by starting with a logical layout one is likely to arrive at a final arrangement which is both logical and economical. Moreover, one is able to see at each stage what one is sacrificing in the way of logical layout in order to achieve economy and vice versa. In order to get some idea of the number of micro-orders required I have constructed a micro-programme for a simple machine with the following orders: add, subtract, multiply (two orders, one for the multiplier, one for the multiplicand), right and left shift (any number of places), transfer from the accumulator to the store, conditional operation depending on the sign of the number in the accumulator, conditional opera- tion depending on the sign of the number in the B register (one B register is assumed), transfer from the store to the B register, input, and output. The micro-programme also provides for the preliminary extraction of the order from the store (Stage 1 in E.D.S.A.C. terminology). Only 40 micro-orders are required to perform all these operations. The considerations involved in drawing-up a micro-pro- gramme resemble those involved in drawing-up an ordinary programme. The final details of the control are thus settled by a systematic process instead of by the usual ad hoc procedures based on the use of block diagrams. Of course, sound engineer- ing would be necessary to produce designs for the decoding Part II tree and the matrices which could be used for any desired micro-programme by arranging the rectifiers suitably in the matrices. One important advantage of this method of design- ing the control is that the order code need not be decided on finally until a late stage in the construction of the machine; it would even be possible to change it after the machine had been put into operation simply by rewiring the matrices. If desired some of the micro-orders can be made conditional in their action as well as (or instead of) conditional as regards the switching of micro-control. This can be done by making the output of the decoding tree branch before it enters matrix A. I doubt if much economy can be achieved this way and if it is done to any extent the advantage that micro- programming resembles ordinary programming is lost. Other variants of the scheme as I have described it will no doubt occur to you. The matrices may be regarded as very high-speed stores holding fixed information. If they could be replaced by an erasable store to which information could be transferred from the main store of the machine when required we should have a machine with no fixed order code; the programmer would, in fact, be able to choose his order code to suit his own requirements and to change it during the course of the pro- gramme if he considered it desirable. Such a machine would have a number of fascinating possibilities but I doubt whether, in view of the amount of equipment it would doubtless involve, its construction could be justified.