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By a proper selection of source and sink lines and choice of constants, it is possible to obtain from the
Fredkin gate other elementary Boolean functions, such as OR, NOT, and FAN-OUT (Figure 6). In order to
synthesize more complex functions one needs circuits containing several occurrences of the Fredkin gate.
For example, Figure 7 illustrates a l-line-to-4-line demultiplexer. Because of the delays represented by the
wires, this is formally a sequential network. However, since no feedback is present and all paths from the
argument to the result traverse the same number of unit wires, the analysis of this circuit is substantially
identical to that of a combinational network.4 Figure 6. Realization of the (a) OR, (b) NOT, and (c) FAN-OUT functions by means of the Fredkin gate. Figure II.15: “Realization of the (a) OR, (b) NOT, and (c) FAN-OUT functions by means of the Fredkin gate.” (Fredkin & To↵oli, 1982)
Figure 6. Realization of the (a) OR, (b) NOT, and (c) FAN-OUT functions by means of the Fredkin gate. Figure 7. 1-line-to 4-line demultiplexer. The "address" lines A0, A1 specify to which of the four outputs Figure 7.F1-line-to 4-line demultiplexer. The "address"here theTheA1 shappen toto which0ofA1lines.) outputs
igure II.16: "data" signal X is4-line demultiplexer. A0, lines pecify lines A , thespecY0,....,Y3 the “1-line-to to be routed. (Note that lines sink ‘address’ echo the address four
Y0,....,Y3 the "data" signal Xtheto be routed. (Note, that ,herethe ‘data’ signal X is to bethe address lines.)
ify to which of is four outputs Y0 . . . Y3 the sink lines happen to echo routed. (Note that here the sink lines happen to echo the address lines.)” (Fredkin
& To↵oli, 1982) ¶2. In general, one function can be embedded in another by providing appropriate constants from a source and ignoring some of the outputs,
The composition rules of conservative logic force one to explicitly consider the distributed delays
the sink which signal from one processing element to the next. In conventional sequential
encountered in, routing a are considered garb...
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This document was uploaded on 03/14/2014 for the course COSC 494/594 at University of Tennessee.
- Fall '13