A 1.8V 1.1-GHZ Novel 8 X 8-Bit Digital Multiplier

This thesis presents the design of an 8x8-bit novel multiplier, which can provide a better performance that its counterparts in the sense that it has a fraction of the silicon area, delay and power consumption of the common architectures such as the conventional linear array multipliers. At the system-level high performance is obtained by implementing a pair-wise multiplication algorithm. Also, parallel addition algorithm is used to add up partial products. Combining these two algorithms results in an efficient cell-based circuit realization. In the circuit-level, pseudo-NMOS full adder cell is chosen amongst the several existing full adder cells due to its superior speed and power performance. The performance of this design has been evaluated by comparing it to those of the recently reported multipliers. The results of the comparison, both in theory and simulation, prove the superiority of the proposed multiplier.

A 1.8V 1.1-GHZ Novel 8 X 8-Bit Digital Multiplier

This thesis presents the design of an 8x8-bit novel multiplier, which can provide a better performance that its counterparts in the sense that it has a fraction of the silicon area, delay and power consumption of the common architectures such as the conventional linear array multipliers. At the system-level high performance is obtained by implementing a pair-wise multiplication algorithm. Also, parallel addition algorithm is used to add up partial products. Combining these two algorithms results in an efficient cell-based circuit realization. In the circuit-level, pseudo-NMOS full adder cell is chosen amongst the several existing full adder cells due to its superior speed and power performance. The performance of this design has been evaluated by comparing it to those of the recently reported multipliers. The results of the comparison, both in theory and simulation, prove the superiority of the proposed multiplier.

Invariance and parallel sums

In this paper, the notions of invariance and parallel sums as defined by Anderson and Duffin for matrices [Series and parallel addition of matrices, J. Math. Anal. Appl. 26 (1969) 576–594] are generalized to von Neumann regular rings.

MINIMAL NON-INTEGER ALPHABETS ALLOWING PARALLEL ADDITION

Parallel addition, i.e., addition with limited carry propagation has been so far studied for complex bases and integer alphabets. We focus on alphabets consisting of integer combinations of powers of the base. We give necessary conditions on the alphabet allowing parallel addition. Under certain assumptions, we prove the same lower bound on the size of the generalized alphabet that is known for alphabets consisting of consecutive integers. We also extend the characterization of bases allowing parallel addition to numeration systems with non-integer alphabets.