Arithmetic with Signed Analog Digits
نویسندگان
چکیده
This paper presents mathematical foundtions of the Overlap Resolution Number System (ORNS) which employs signed Continuous Valued Digits (CVD’s). ORNS is a redundant Number System employing residue arithmetic. In contrast to the implementation of arithmetic by binary or multiple-valued logic circuits, arithmetic operations in this novel number system are performed by analog digit manipulation circuitry. The redundancy in an ensemble of Continuous Valued Digits that comprises a number, provides tolerance to implementation imprecisions. Processing with these analog digits implies carry-free arithmetic structures with systematic redundancy.
منابع مشابه
A Number System with Continuous Valued Digits and Modulo Arithmetic
This paper presents a novel number system based on signed continuous valued digits. Arithmetic operations in this number system are performed using simple analog circuitry, in contrast to the conventional implementation of arithmetic units by Boolean or multiple-valued logic circuits. Unlike the limited precision offered by classical analog arithmetic circuits, the ensemble of continuous valued...
متن کاملArithmetic Circuits for Analog Digits
The Overlap Resolution Number System (ORNS) employs bit level residue arithmetic, and opens up a powerful approach to digital computing with analog processing elements. This new redundant representation of signals, with Continuous Valued Digits, opens up new methods for binary arithmetic and digital signal processing. The number system is based on analog residues as opposed to binary or multipl...
متن کاملDesign and Synthesis of High Speed Low Power Signed Digit Adders
Signed digit (SD) number systems provide the possibility of constant-time addition, where inter-digit carry propagation is eliminated. Such carry-free addition is primarily a three-step process; adding the equally weighted SDs to form the primary sum digits, decomposing the latter to interim sum digits and transfer digits, which commonly belong to {–1, 0, 1}, and finally adding the tra...
متن کاملCombinational arithmetic systems for the approximation
The concepts of arithmetic building blocks (ABB) and combinational arithmetic (CA) nets as well as their applications have been previously reported in References 3, 4, and 5. The unique ABB, resulting from the efforts of minimizing the set of building blocks in Reference 3, is designed at the arithmetic level, employing the redundant signed-digit number system,2 and is to be implemented as one ...
متن کاملQuaternary Arithmetic Logic Unit on a Programmable Logic Device
Common binary arithmetic operations such as addition/subtraction and multiplication suffer from O(n) carry propagation delay where n is the number of digits. Carry lookahead helps to improve the propagation delay to O(log n), but is bounded to a small number of digits due to the complexity of the circuit. A carry-free arithmetic operation can be achieved using a higher radix number system such ...
متن کامل