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Majority logic formulations for parallel adder designs at reduced delay and circuit complexity
Published in IEEE Computer Society
2017
Volume: 66
   
Issue: 10
Pages: 1824 - 1830
Abstract
The design of high-performance adders has experienced a renewed interest in the last few years; among high performance schemes, parallel prefix adders constitute an important class. They require a logarithmic number of stages and are typically realized using AND-OR logic; moreover with the emergence of new device technologies based on majority logic, new and improved adder designs are possible. However, the best existing majority gate-based prefix adder incurs a delay of 2log2 (η) 1 (due to the nth carry); this is only marginally better than a design using only AND-OR gates (the latter design has a 2log2 (η) 1 gate delay). This paper initially shows that this delay is caused by the output carry equation in majority gate-based adders that is still largely defined in terms of AND-OR gates. In this paper, two new majority gate-based recursive techniques are proposed. The first technique relies on a novel formulation of the majority gate-based equations in the used group generate and group propagate hardware; this results in a new definition for the output carry, thus reducing the delay. The second contribution of this manuscript utilizes recursive properties of majority gates (through a novel operator) to reduce the circuit complexity of prefix adder designs. Overall, the proposed techniques result in the calculation of the output carry of an n-bit adder with only a majority gate delay of log2 (η) 1. This leads to a reduction of 40percent in delay and 30percent in circuit complexity (in terms of the number of majority gates) for multi-bit addition in comparison to the best existing designs found in the technical literature. © 1968-2012 IEEE.
About the journal
JournalData powered by TypesetIEEE Transactions on Computers
PublisherData powered by TypesetIEEE Computer Society
ISSN00189340
Open AccessNo
Concepts (15)
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    Adders
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    CARRY LOGIC
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    Computer circuits
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    Delay circuits
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    Logic circuits
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    Timing circuits
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    ARITHMETIC COMPLEXITY
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    CARRY
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    Emerging technologies
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    HIGH PERFORMANCE ADDERS
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    MAJORITY VOTING LOGIC
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    PARALLEL PREFIX ADDER
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    RECURSIVE TECHNIQUES
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    TECHNICAL LITERATURE
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    MAJORITY LOGIC