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Radix-8 Design Alternatives of Fast Two Operands Interleaved Multiplication with Enhanced Architecture


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Figure 1.

Carry save Adder: (a) Top View Design (b) Internal Architecture
Carry save Adder: (a) Top View Design (b) Internal Architecture

Figure 2.

Delay-Area analysis of CSA vs CLA implementations (8–64 bit)
Delay-Area analysis of CSA vs CLA implementations (8–64 bit)

Figure 3.

Kogge Stone Adder: (a) Top View Design of KSA (c) KSA Stages (c) Group generation and propagation
Kogge Stone Adder: (a) Top View Design of KSA (c) KSA Stages (c) Group generation and propagation

Figure 4.

Dot notation of Multi-operand addition for multiplication and inner-product computation
Dot notation of Multi-operand addition for multiplication and inner-product computation

Figure 5.

Multi-operand addition for 10 operands.
Multi-operand addition for 10 operands.

Figure 6.

Aligning Partial Products.
Aligning Partial Products.

Figure 7.

The complete design of8- Bit Comparatorincluding Pre- Encoding circuit and Comp circuit
The complete design of8- Bit Comparatorincluding Pre- Encoding circuit and Comp circuit

Figure 8.

Design of Radix-8 Booth 32-bit multiplier
Design of Radix-8 Booth 32-bit multiplier

Figure 9.

State machine diagram for 32-bit Booth multiplier.
State machine diagram for 32-bit Booth multiplier.

Figure 10.

Design of 64-bit CSA Based Radix-8 Booth, Wallace Tree Karatsuba multiplier.
Design of 64-bit CSA Based Radix-8 Booth, Wallace Tree Karatsuba multiplier.

Figure 11.

Graphical approaches to demonstrate the carry error (the mid-carry problem), here we have two cases: Case I- ps1+ pc1 = might result in carry, result = 65-bit (wrong). Carry must be discarded and Case II- ps1+ ps2 = might result in carry, result = 65-bit (correct). Carry must be considered.
Graphical approaches to demonstrate the carry error (the mid-carry problem), here we have two cases: Case I- ps1+ pc1 = might result in carry, result = 65-bit (wrong). Carry must be discarded and Case II- ps1+ ps2 = might result in carry, result = 65-bit (correct). Carry must be considered.

Figure 12.

Design of 64-bit: 64-bit CSA Based Radix-8 Booth, KSA Based Karatsuba multiplier.
Design of 64-bit: 64-bit CSA Based Radix-8 Booth, KSA Based Karatsuba multiplier.

Figure 13.

Karatsuba multiplication based on CSA and comparator.
Karatsuba multiplication based on CSA and comparator.

Figure 14.

Design of CSA based Radix-8 Booth 64-bit multiplier.
Design of CSA based Radix-8 Booth 64-bit multiplier.

Figure 15.

(a) Design Architecture of WCBM (a) Top Level DiagramWCBM (C) FSM Diagram for WCBM.
(a) Design Architecture of WCBM (a) Top Level DiagramWCBM (C) FSM Diagram for WCBM.

Figure 16.

Sample run example of WCBM process of two 64-bit numbers
Sample run example of WCBM process of two 64-bit numbers

Figure 17.

Waveform sample of the proposed WCBM data delay
Waveform sample of the proposed WCBM data delay

COMPARISON BETWEEN DESIGN II & DESIGN III.

Design Solutions # Delay (gate delay) % Optimization Area (# of gates) % Optimization
Solution I: using KSA Adder. 23 +15% 6130  
Solution II: using Comparator unit. 27   3712 +50%

RADIX-8 BOOTH ENCODING.

Inputs (bits of M-bit multiplier) Partial Product
xi+2 xi+1 xi xi−1 PPRi
0 0 0 0 0
0 0 0 1 A
0 0 1 0 A
0 0 1 1 2A
0 1 0 0 2A
0 1 0 1 3A
0 1 1 0 3A
0 1 1 1 4A
1 0 0 0 -4A
1 0 0 1 -3A
1 0 1 0 -3A
1 0 1 1 -2A
1 1 0 0 -2A
1 1 0 1 -A
1 1 1 0 -A
1 1 1 1 0
eISSN:
2470-8038
Idioma:
Inglés
Calendario de la edición:
4 veces al año
Temas de la revista:
Computer Sciences, other