This document describes the design of a parallel self-timed adder called PASTA that uses a recursive approach. PASTA performs multi-bit binary addition without needing any carry chain propagation. It works by first accepting two input operands and performing half additions for each bit, then iteratively using the previous sums and carries to perform additional half additions until all carries settle to zero. The architecture of PASTA uses multiplexers to select between the actual operands and feedback paths from previous half additions. Simulation results show its advantages over traditional approaches in reducing delay and improving efficiency.

1. RECURSIVE APPROACH TO THE
DESIGN OF A PARALLEL
SELF-TIMED ADDER
By
Ms. D.Vidya (14C35A0409)
Ms. V.Pavanisujatha (13C31A04A1)
Mr.P.Chendra shekar (13C31A0471)
Under the guidance of
Ms. M. Mounika
Assistant professor
BALAJI INSTITUTE OF TECHNOLOGYAND SCIENCE
NARSAMPET, WARANGAL – 506 331
DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING

2. CONTENT
• INTRODUCTION
• ABSTRACT
• DESIGN OF PASTA
• ARCHITECTURE OF PASTA
• STATE DIAGRAMS FOR PASTA
• FLOW CHART
• RECURSIVE FORMULA FOR BINARY ADDITION
• SIMULATION WAVE FORM FOR RECURSIVE ADDER
• SYNTHESIS REPORT FOR RECURSIVE ADDER
• APPLICATIONS
• ADVANTAGES
• CONCLUSION

3. INTRODUCTION
• Binary addition is the single most important operation that a
processor performs.
• Asynchronous circuits do not assume any quantization of
time.
• In principle, logic flow in asynchronous circuits is controlled
by a request-acknowledgment handshaking protocol to
establish a pipeline in the absence of clocks.

4. ABSTRACT
• It is based on a recursive formulation for performing multi-bit
binary addition.
• Do not need any carry chain propagation.
• Does not have any practical limitations of high fan-outs.
• A high fan-in gate is required though but this is unavoidable
for asynchronous logic and is managed by connecting the
transistors in parallel.

5. DESIGN OF PASTA
• The adder first accepts two input operands to perform half
additions for each bit.
• Subsequently, it iterates using earlier generated carry and sums
to perform half-additions repeatedly until all carry bits are
consumed and settled at zero level.

6. ARCHITECTURE OF PASTA

7. Cont….
• Initially it select the actual operands during SEL = 0 and
switch to feedback/carry paths for subsequent iterations using
SEL = 1.
• The feedback path from the HAs enables the multiple
iterations to continue until the completion when all carry
signals will assume zero values.

8. State Diagram for PASTA

9. Cont…..
• During the initial phase, the circuit merely works as a
combinational HA operating in fundamental mode.
• During the iterative phase (SEL = 1), the feedback path
through multiplexer block is activated.
• The carry transitions (Ci ) are allowed as many times as
needed to complete the recursion.

10. FLOW CHART

11. Recursive Formula for Binary Addition
• Sj
i and Cj
i+1 are the sum and carry for ith bit at the jth
iteration.
• The initial condition ( j = 0) for addition is formulated as
follows:
S0
I = ai ⊕ bi
C0
i+1= ai bi .

12. • The jth iteration for the recursive addition is formulated by
Sj
i = S j−1
i ⊕ C j−1
i , 0 ≤ i < n
C j
i+1 = S j−1
i C j−1
i , 0 ≤ i ≤ n.
• The recursion is terminated at kth iteration when the following
condition is met:
Ck
n + Ck
n−1+ ・・ ・+Ck
1= 0, 0 ≤ k ≤ n.

13. SIMULATION WAVE FORM FOR
RECURSIVE ADDER

14. SYNTHESIS REPORT FOR RECURSIVE
ADDER

15. APPLICATIONS
• Digital systems designing
• Digital signal processing
• Multiplication and Accumulation
• Arithmetic and Logic Unit (ALU)
• Microprocessors

16. ADVANTAGES
• Delay will be reduced.
• Area Efficient adders.

17. CONCLUSION
• The design achieves a very simple n-bit adder that is area and
interconnection-wise equivalent to the simplest adder namely
the RCA.
• Moreover, the circuit works in a parallel manner for
independent carry chains, and thus achieves logarithmic
average time performance over random input values.
• Simulation results are used to verify the advantages of the
proposed approach.

18. Any Queries??????