By Topic

On Nonlinear Binary Sequential Circuits and Their Inverses

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

2 Author(s)
Reiffen, B. ; Lincoln Laboratory, Massachusetts Institute of Technology, Lexington, Mass. ; Yudkin, H.L.

This paper discusses single-input, single-output binary sequential circuits composed of adders, multipliers and delay units. The principal results are: 1) Finite feedforward circuits are characterized by a response function (rf) which permits the determination of the output for an arbitrary input. 2) Corresponding to every rf is a transfer function (tf) which is obtained by a multidimensional Z-transform of the rf. This tf permits the determination of the response of a feedforward circuit by transform domain techniques. 3) Every tf may be synthesized as a physical circuit. 4) A canonic form is defined for every tf. With this canonic form is identified an implementation which contains a minimum number of delay units and adders. 5) Nonfeedforward circuits are called well defined if they meet certain physically meaningful restrictions. 6) Well-defined circuits may be classified as those which have inverses (class I) and those which do not. Membership in class I is shown to be a property of circuits which established one-one maps of inputs onto outputs. Circuits which do not belong to class I have neither left nor right inverses. 7) An intimate connection between inverses and feedback circuits is established. It is shown that any well-defined feedback circuit and a related circuit in I are mutually inverse. 8) It is shown that the necessary and sufficient condition for a feedback circuit to be well defined is that the circuit in the feedback loop contains delay.

Published in:

Electronic Computers, IEEE Transactions on  (Volume:EC-15 ,  Issue: 4 )