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ship to these principles, will help to produce a better and is automatically transferred to the product register
understanding of the functioning of the machine. each time the multiplier becomes an odd number.
Binary notation is the notation of numbers in the
scale of two, the carry, or point at which the same sym-
bols are used over again, occurs after the tenth in
decimals but after the second symbol in Binary.
If the figures 1 + 1 are added in Binary, it will not
give the answer 2 as a decimal, but 0 and carry 1, which
would be written as 10. We thus see that whilst 1
represents 1, 10 represents 2.
Similarly, if 10 + 10 are added in Binary, the answer
will be 100, and this therefore represents the figure 4. Fig. 17. Multiplication of 56 by 23.
Thus, each digit is twice as great as the one on its right.
Consider the Binary figure 1111, this then represents Consider an example:- 56 X 23 = 1288.
in order reading from the left the figures 8, 4, 2, 1 and, Multiplicand Product
to find its equivalent in decimal, these figures are added (doubled) Multiplier (halved) accumulated
giving 15. 56 23 since odd transfer 56
112 11 since odd transfer 168
224 5 since odd transfer 392
448 2 since even no transfer 392
896 1 since odd transfer 1288
1792 0 zero no transfer 1288
Total
After each halving operation the remainders arc
dropped.
Fig. 16. Addition and Subtraction in Binary.
Addition Fig. 18. The Five Main Components for Multiplication.
This is quite straight forward, simply add 1 to 1 and This shows the five main components necessary for
carry. multiplication:-
Subtraction (1) The Multiplier Register-thisholds the figure
This may at first appear to be more difficult, but to be halved.
instead of subtracting, the machines find the comple- (2) The Multiplicand Register-thisholds the
ment of the subtractor and add it. To find the com- figure to be doubled.
plement of a figure in Binary simply means to subtract (3) The Product Register-thisaccumulates the
it from 15-thusthe complement of 6 would be 9 and amounts it receives from the multiplicand
the complement of 4 would be 11. register.
Multiplication (4) The Adder-thisadds the amounts in the
The method by which multiplication is performed is multiplicand to the product.
that known as "Halving and Doubling," the multiplier (5) The Odd-Even Detector (OED)-thisallows
is repeatedly halved until it reaches zero, while simul- a transfer from the multiplicand to the product
taneously the multiplicand is doubled. The multiplic- only when the multiplier is an odd number.
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Doubling
Fig. 21. Schematic arrangement of Halving and
Numerical Example.
Fig. 19. Schematic arrangement for Doubling. must be added into the register position below. This
can best be shown by the example:-
All that is required to double a number is to shift 50 ÷ 2 = 25.
it one place to the left, the feed back loops of the
multiplicand register are connected so that when doub- Arrangement of Machine
ling, the "1" feeds back to the "2," the "2" feeds
back to the "4," the "4" to the "8," and the "8"
to the Carry Memory buss bar. The 4, 2 and 1 lines
are connected via the half adder to the C.M., since a
combination of 4 and any other figure when doubled
will require this circuit.
We have chosen the example No. 936 as this entails
the use of the Carry Memory.
Fig. 22. Basic arrangement of Arithmetic Unit.
This shows the five stores, the three registers, the
adder, the complementer and the emitter. The emitter
can be used to insert a figure into any of the registers
which would be common to a series of cards.
It will be noticed that there are two paths, A and B
-thisenables the machine to add together the quanti-
Fig. 20. Example of Doubling the number 936. ties held in stores 2, 3, 4 and 5 to store 1, thus enabling
the calculation of the type (A + B) times C to be
carried out as it were in one run. The stores, with the
Halving exception of No. 1, can pass through the complementer.
To halve the number in the multiplier register each Shifting Registers
Binary expressed denomination is shifted one position
to the right, but as no decimal digit after halving can
One of the fundamentals of valve registers is that of
exceed 9, there will be no carry up the register, and being able to transfer (or shift) the digit in one position
therefore the "ten" detector and rationalising circuits to the next position, and so on through all the stages of
are not needed. One bank of adders is necessary, how- the register. The shifting registers are composed of a
ever, because when a register position (other than the series of inter-connected triggers, one series for each
units position) holds a digit that is an odd number, a 5 register position.
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