Array Synthesis in SystemC Hardware Compilation

Decimal Multiplier on FPGA using Embedded Binary Multipliers Authors: H. Neto and M. Vestias Conference: Field Programmable Logic and Applications (FPL), 2008 Presenter: Tareq Hasan Khan ID: 11083577 ECE, U of S Literature review-3 (EE 800) Outline

Motivation Proposed Binary-BCD conversion using base-1000 algorithm BCD multiplier Results Conclusion 2 Motivation

Decimal arithmetic Human centric application Precisely present decimal fractions Software implementations of decimal arithmetic are slower than in hardware Proposing a BCD multiplier

BCD operands will be converted to Binary Taking advantage of the efficient embedded binary multipliers (17x17) available in state-of-the-art FPGAs. A novel method to convert from Binary to BCD is proposed 3 Outline

Motivation Proposed Binary-BCD conversion using base-1000 algorithm BCD multiplier Results Conclusion 4 Binary-BCD conversion using base-1000 algorithm

1. Convert binary number to a number represented in base-1000 2. Convert each base-1000 digit to BCD using the shift and add-3 algorithm 5 Conversion of Binary number to base-1000

6 Conversion of Binary number to base-1000cont. 7 Binary to base-1000 conversion hardware up to 999x999 b1 b1 c1

d1^ b0 c0 d0^ 8 Binary to base-1000 conversion for higher numbers

The algorithm can be applied iteratively to convert larger binary numbers to base-1000 Each digit of the result in base-1000, is calculated iteratively according to Horners rule 9 Binary to base-1000 conversion hardware up to 9999 x 9999 10

Binary to base-1000 conversion hardware up to 99999 x 99999 Multipliers of 17 17 size are found on state-of-the-art FPGAs as embedded multipliers. Binary multiplication of 17 17 without sign will result 34 bits. Base-1000 digits are converted to BCD by Shift and Add-3 algorithm 11 Outline

Motivation Proposed Binary-BCD conversion using base 1000 BCD multiplier Results Conclusion 12

BCD multiplier Convert each BCD operands to binary Multiply the binary numbers using embedded FPGA binary multiplier

Convert the binary result to BCD using the proposed binary to BCD through base-1000 algorithm 13 BCD multipliercont 14 Outline

Motivation Proposed Binary-BCD conversion using base 1000 BCD multiplier Results Conclusion 15

Result Implemented on Xilinx Virtex-4 SX35-12 FPGA Area increases almost linearly with number of BCD digits Frequency goes from 242 to 222 MHz Two levels of pipeline 16

I1 - A binary to base-1000 converter and then a parallel shift and add-3 algorithm for each b-1000 digit I2 - A binary to decimal converter using the parallel shift and add-3 algorithm. I3 - A binary to decimal converter using the serial shift and add-3 algorithm

Resultcont I1 (proposed) uses less area (about 60%) than the commonly used I2 I3 has a very low area occupation, high speed, but higher latency 17 Resultcont2

Mult1 - Decimal multiplier with converter I1 (proposed) Mult2 - Decimal multiplier with converter I2 Mult3 - Decimal multiplier via carry-save addition

Mult1 (proposed) uses less area (about 65%) than the commonly used Mult2 Mult1 uses (about 70%) area than Mult3, at the cost of an embedded binary multiplier All implementation work at frequency near 200MHz 18 Conclusion Proposed Binary-BCD conversion

algorithm using base-1000 More area efficient than mostly used shift and add-3 algorithm BCD multiplier implemented in this work, take advantage of embedded binary multipliers on state-of-the-art FPGAs 19 Thanks

20 24.X + Y hardware block 21