As digital systems continue to grow, verification of these systems is becoming an increasingly important and difficult problem. To ensure a quick time-to-market, the verification problem must be addressed early in the design cycle. This requires the ability to verify systemlevel descriptions of hardware and embedded software systems, such as, C or Verilog, by proving assertions and proving func...

We present a unified mixed radix CORDIC algorithm with carry-save arithmetic with a constant scale factoi. The pipelined architecture of the processor is determined by a unique sequence of microrotations for the two modes of operation (rotation and vectoring) in circular and hyperbolic coordinates. The combination of radix-2 and radix-4 microrotations allows us to reduce the latency and size of...

Modular multiplication is the main and basic operation in public key cryptography algorithms like Elliptic Curve Cryptography (ECC). By using Residue Number System (RNS) in these algorithms, large number computation is replaced by computation over the small moduli without carry propagation between moduli. Moduli selection has an important role in the efficiency of modular multiplication. Theref...

We present an automated veriication technique for veriica-tion of concurrent linked lists with integer variables. We show that using our technique one can automatically verify invariants that relate (unbounded) integer variables and heap variables such as head 6 = null ! numItems > 0. The presented technique extends our previous work on composite symbolic representations with shape analysis. Th...

A high-speed 64-bit binary comparator is proposed in this brief. Comparison is most basic arithmetic operation that determines if one number is greater than, equal to, or less than the other number. Comparator is most fundamental component that performs comparison operation. This brief presents comparison of modified and existing 64-bit binary comparator designs concentrating on delay. Means so...

Complex tensor contraction expressions arise in accurate electronic structure models in quantum chemistry, such as the Coupled Cluster method. Transformations using algebraic properties of commutativity and associativity can be used to significantly decrease the number of arithmetic operations required for evaluation of these expressions, but the optimization problem is NP-hard. Operation minim...

High-speed tree-based 64-bit binary comparator: A New Approach is proposed in this brief. Comparison is most basic arithmetic operation that determines if one number is greater than, equal to, or less than the other number. Comparator is most fundamental component that performs comparison operation. This brief presents comparison of modified and existing 64-bit binary comparator designs concent...

A high-speed tree-based 64-bit CMOS binary comparator is proposed in this brief. Comparison is most basic arithmetic operation that determines if one number is greater than, equal to, or less than the other number. Comparator is most fundamental component that performs comparison operation. This brief presents comparison of modified and existing 64-bit binary comparator designs concentrating on...

High-speed 64-bit binary comparator using two stages with two different logic styles is proposed in this brief. Comparison is most basic arithmetic operation that determines if one number is greater than, equal to, or less than the other number. Comparator is most fundamental component that performs comparison operation. This brief presents comparison of modified and existing 64-bit binary comp...

Brain activation was examined using functional magnetic resonance imaging during mathematical problem solving in 7 young healthy participants. Problems were selected from the Necessary Arithmetic Operations Test (NAOT; R. B. Ekstrom, J. W. French, H. H. Harman, & D. Dermen, 1976). Participants solved 3 types of problems: 2-operation problems requiring mathematical reasoning and text processing,...