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> Carry Detection and Propagation |
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Carry Detection and Propagation(Eight of each assembly are required) |
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Addition in the difference engine proceeds in two phases. In the first phase, numbers are added digit by digit, and then in the second phase, any carries that were generated in the first phase are added to the result. The pictures below show the assemblies needed to accomplish the detection and subsequent propagation of carries. The axes which carry the digit wheels rotate four revolutions per cycle of the machine. During the phase where digit by digit addition is taking place, if the output digit wheel passes from 9 to 0 then a carry must occur to the next higher digit in the same column. |
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The
components of a carry
assembly are shown below. A face plate with boss down carries a
1½" narrow strip, an angle bracket, and a tension spring, held
on a 3/8" bolt. The angle bracket should be held at the end of the
slotted hole and aligned such that the vertical end is flush with the
edge of the face plate and shown in the picture to the right. The other
end of the tension spring will be slipped over the rod of the carry
axis and provides the force required to set the carry once the pawl is
tripped by the digit wheel advancing from 9 to 0.
Shown on the left, on the underside of the face plate, a ratchet wheel
is
connected by a socket coupling. This assembly must be free to turn on a
rod
so select and adjust parts carefully to make sure there is no binding.
The
assembly is completed by a short threaded pin which carries a ½"
pulley
without boss held in place by a collar. |
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A
total of eight of each of the items described above will be
required. The
pictures below show two views from the rear of the machine of the
components assembled together. Note that between the carry assembly at
the bottom and the carry detector gear at the top is the bolting
assembly. The bolting assembly is the only item rigidly attached to the
rod, the other components are all free to
turn on the rod, held in place by collars. |
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Although
in any given column, carries are only propagated every fourth rotation
of the main crank, the carry axes actually rotate at half the rate of
main crank, though only every second turn actually results in carries
propagating. The reason for this is that carries must ripple up from
the bottom of a column to the top. That is, when a carry adds one to a
digit wheel it is possible that that wheel will, as a result, move form
9 to 0, generating another
carry to the digit above. Thus the carries must be propagated sequentially from digit to digit up the column. To achieve this the carry arms are arranged spirally on the carry axes. In order to get the carry operation completed in one turn of the main crank, the carry axes must revolve more quickly than they would if only making one turn per full cycle of the machine. On every other rotation of the carry axis, since no addition has preceded it, there naturally are no carries to propagate and the carry axis rotates with no action resulting. This is in fact one aspect of the machine that would not scale up directly to numbers of arbitrary numbers of digits. Babbage recognized this in his original plans and to accommodate the time required for the carry propagation he also staggered the digit by digit addition up the columns, which had the desirable side effect that the load on the drive is more uniform. However, for this very small scale model which does not handle large enough numbers for this to be an issue, I preferred the simplicity of having all the digits be added simultaneously, which makes setup and alignment of the machine much simpler. |
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Framework Arrangement of axes and drive system Decimal digit storage Digit readout and addition > Carry detection and propagation Setup and adjustment Operation Parts list |
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