162 Part 2½
Regions of Computer Space Section 1½
Microprogram-Based Processors
up an ordinary programme for an automatic computing machine and the problems involved are very much alike.
4. The Timing of Micro-Operations
The assumption that all micro-operations take the same length of time to perform is not likely to he borne out in practice. In particular in a parallel machine it may not be possible to design an adder in which the carry propagation time is sufficiently short to enable an addition to be performed in substantially the same length of time as that taken for a simple transfer, It will be necessary, therefore, to arrange that the wave-form generator feeding the decoding tree should, when suitably stimulated by a pulse from one of the outputs from matrix A, supply a somewhat longer pulse than that normally required. Other operations may take many times as long to perform as an ordinary micro-order; for example, access to and from the store (particularly if a delay store is used) and operation of the input and output devices of the machine. The sequence of operations in the micro-programme must therefore be interrupted. One way of doing this is to prevent pulses from the wave-form generator reaching the decoding tree during the waiting period. This method, although quite feasible, appears to involve just the kind of complication which the present system is designed to avoid. A more attractive system is to make the machine wait on a conditional micro-order which transfers control back to itself unless the associated conditional flip-flop is set. Setting of this flip-flop takes place when the operation is completed, and control then goes to the next micro-order in the sequence. The machine is thus in a condition of "dynamic stop" while waiting for the operation to be completed. This system has the advantage that no complication is introduced into the units supplying the wave-forms to the decoding tree and that the control equipment required is similar to that already provided for other purposes.
5. Discussion
It will be seen that the equipment needed to execute a complicated order in the machine order code is of the same form as that required for a simple one, namely outlets from the decoding tree and diodes in the matrices. Quite complicated orders can, therefore, be built into the machine without difficulty. In particular, arithmetical operations on numbers expressed in floating binary form and other similar operations can be micro programmed and it is found that they do not involve very large numbers of micro-orders. For example, a micro-programme providing for the floating-point operations of addition, subtraction, and multiplication needs about 70 micro-orders. The switching system in the arithmetical unit must, of course, be designed with these operations in view. The decoding tree and matrices of a parallel machine with 40 digits in the arithmetical unit and provision for 256 micro-orders would only amount to about 15% of the total equipment in the machine, so that it appears that such a machine can well be provided with built-in facilities of considerable complexity.
The number of micro-orders needed in a complicated micro-programme can sometimes be reduced by making use of what might be called micro-subroutines. For example, when two numbers have to be added together in a floating binary machine, some shifting of one of them is usually necessary before the addition can take place. By making the micro-orders for this shifting operation serve also when a multiplication is called for, considerable saving is effected.
Four registers is the bare minimum needed in the arithmetical unit in order to enable the basic arithmetical operations to be performed. If any extension or refinement of the facilities provided is required, it may be necessary to increase the number of registers. For example, four registers are not sufficient to enable a succession of products to be accumulated without the transfer of intermediate results to the store, since the accumulator must be clear at the beginning of a multiplication. The addition of one register enables the accumulation of products to be provided for in the micro-programme. If this register is associated with the outlet from the store, it also enables some of the waiting time for storage access to be eliminated. To do this the micro-programme is arranged to call for a number from the store as soon as it is known that the number will be required and to continue with other necessary micro-operations before finally proceeding to use the number. The "dynamic stop" would occur just before the number is required for use. Another way of saving time is to arrange, in the case of those orders which permit it, for the next order to be extracted from the store before the operation currently being performed has been completed.
The minimum number of registers required in the control register unit of the machine for the simplest mode of operation is three. If extra registers are provided facilities similar to those provided by the B-lines in the machine at Manchester University could be included in the micro-programme.
6. Microprogramming Applied to Serial Machines
All the discussion so far as been with reference to parallel machines because the technique described in this paper is most adapted to that type of machine. It is, however, possible to design a serial machine along the same lines. In a parallel computer with