Abstract: Logic elements for use in carry/borrow and comparator systems, which operate in accordance with the IMPLY logical relationship. Utilization of the IMPLY logical relationship overcomes the inherent complication of inversion so that it becomes an effective benefit, making possible uniform carry system layouts with uniform logic elements using a newly defined gate pair combination in general. The gate pair logic elements provide a novel carry-propagate signal (P) which includes a redundant carry-generate signal (G), thereby defining a novel carry-integrate signal (I) . The novel carry-integrate, signal (I) together with the carry-generate signal (G) define a signal pair utilized in succeeding carry levels which are organized in a simplified fashion. For-2-bit position (i+1, i) positive sense logic, the carry-integrate signal can be represented by I(i+1, i)=G(i+1)+P(i+1). P(i)) . Wherever the IMPLY relationship is involved in logic functions, the design of CMOS gates is affected and can be modified.

Abstract: A multi-bit arithmetic logic unit having a fast carry-look-ahead (CLA) system comprises logical preparation (LLP) circuitry of the first CLA level which interconnects several bit positions so as to output intermediate combination signals which are a function of a plurality of bit positions, rather than of a single bit position. In addition, the carry-in signal (C.sub.IN) into the least-significant-bit (LSB) of the respective group is separated from the intermediate combined propagated carry signal (C.sub.p) between groups, and is introduced into the input of the LLP circuitry of the first CLA level, combined with the LSB signals, and also with a binary "split" signal whose state determines whether the C.sub.IN is to be inputted or not.

Abstract: A selectably positionable rotary transducer including a first member having at least one permanent magnet associated therewith and a second member arranged for rotational motion relative to the first member in a first plane, the second member defining an odd number of poles and associated apparatus for selectively providing a magnetic force of selected polarities to individual ones of the poles to cause the first member to assume selectable positions with respect to the second member. Numbering apparatus preferably having an odd number of poles is also described.