Majority Logic Formulations for Parallel Adder Designs at Reduced Delay and Circuit Complexity - 2017


The planning of high-performance adders has experienced a renewed interest in the previous couple of years; among high performance schemes, parallel prefix adders constitute an necessary category. They need a logarithmic range of stages and are typically realized using AND-OR logic; moreover with the emergence of recent device technologies based on majority logic, new and improved adder styles are attainable. But, the simplest existing majority gate-primarily based prefix adder incurs a delay of 2log2(n) - one (due to the nth carry); this is often only marginally higher than a style using only AND-OR gates (the latter design incorporates a 2log2(n) + 1 gate delay). This paper initially shows that this delay is caused by the output carry equation in majority gate-primarily based adders that's still largely defined in terms of AND-OR gates. During this paper, two new majority gate-primarily based recursive techniques are proposed. The first technique depends on a unique formulation of the bulk gate-based mostly equations in the used group generate and cluster propagate hardware; this leads to a brand new definition for the output carry, thus reducing the delay. The second contribution of this manuscript utilizes recursive properties of majority gates (through a unique operator) to cut back the circuit complexity of prefix adder designs. Overall, the proposed techniques lead to the calculation of the output carry of an n-bit adder with only a majority gate delay of log2 (n) + one. This results in a discount of 40percent in delay and 30percent in circuit complexity (in terms of the amount of majority gates) for multi-bit addition as compared to the best existing styles found within the technical literature.

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