We explore the use of subfield arithmetic for efficient implementations of Galois Field arithmetic especially in the context of the Rijndael block cipher. Our technique involves mapping field elements to a composite field representation. We describe how to select a representation which minimizes the computation cost of the relevant arithmetic, taking into account the cost of the mapping as well...

This paper describes the logical structure of the RC 4000, a 24-bit, binary computer designed for multiprogramming operation. The design is characterized by multiple accumulators, expandable storage, low-speed and high-speed data channels, storage protection, and program interruption. Processing operations include byte manipulation, word comparison, and integer and floating-point arithmetic. Ty...

Speed of digital arithmetic processor depends mainly on the speed of adders. This paper provides a technique so that we can increase the speed of addition. Hybrid signed digit number representation perform addition in such a way that the carry propagation chain is limited to single digit position and hence are used to speed up arithmetic operation. Also hybrid signed digit reduces the critical ...

Speed of digital arithmetic processor depends mainly on the speed of adders. This paper provides a technique so that we can increase the speed of addition. Hybrid signed digit number representation perform addition in such a way that the carry propagation chain is limited to single digit position and hence are used to speed up arithmetic operation. Also hybrid signed digit reduces the critical ...

Basic arithmetic is the cornerstone of mathematics and computer sciences. In arithmetic, ‘division by zero’ is an undefined operation and any attempt at extending logic for algebraic division to incorporate division by zero has resulted in paradoxes and fallacies. However, there is no proven theorem or mathematical logic that suggests that, defining logic for division by zero would result in br...

The objective of this work is to investigate the cognitive development of semantic process and arithmetic calculation in childhood using event-related potential tools. Sixty children of three age groups (8-, 9and 11-year-old groups) participated in the experiment. Each group included 10 girls and 10 boys. Stimuli were presented in two separate lists: semantic priming list and mental arithmetic ...

The residue number system (RNS) has computational advantages for large integer arithmetic because of its parallel carry free, and high-speed arithmetic nature. However, magnitude comparison is a very complex operation for RNS. This paper presents a new comparison algorithm based on the modification of Mixed-Radix Conversion II technique. The new algorithm uses small modulo operations only and h...

The extension principle defines the arithmetic operations on fuzzy numbers. In the extension principle one can use any t-norm for modeling the conjunction operator. It is therefore important to know, which t-norms are consistent with a particular type of fuzzy number. We call a t-norm consistent, if the arithmetic operation is closed. In this paper we investigate the addition of sigmoid and two...

In this paper we study applicative theories of operations and numbers with (and without) the non-constructive minimum operator in the context of a total application operation. We determine the proof-theoretic strength of such theories by relating them to well-known systems like Peano Arithmetic PA and the system ((0 1-CA) <"0 of second order arithmetic. Essential use will be made of so-called x...