altera corporation 1 round data word rounder february 1997, ver. 1 functional speci?ation 5 a-fs-05-01 features n round reference design implementing a data word rounder n parameterized input and output widths n optimized for flex 10k and flex 8000 device families n rounds arbitrary-length words to shorter words n signed (two's complement) or unsigned operation n built-in post-round adder n supported by max+plus ii n useful for a variety of applications, including digital filters, image processing, and video processing general description in most digital signal processing (dsp) systems, word length and word growth effects are important aspects of design. because the result of a calculation often contains more bits than is desired, some method must be used to reduce the number of significant bits in a particular data path. although simple truncation of the least significant bits (lsbs) is the easiest method to use, it produces excess noise in the lsb. the round function uses a technique of truncation and rounding to decrease the number of significant bits while minimizing noise. figure 1 shows the symbol for the round reference design. figure 1. round symbol the concept of rounding binary digits is the same as rounding decimal digits. if the digit to the right of the decimal point is greater than 0.5, round the digit up; otherwise, round the digit down. for example, rounding the decimal number 1.25 (01.01 b ) yields 1 (01 b ), and rounding the decimal number 1.75 (01.11 b ) yields 2 (10 b ). dataa[ ] datab[ ] result[ ] cout overflow widthi= representation= widthr= round
2 altera corporation fs 5: round data word rounder the round reference design accepts any bit-width number and properly rounds it to a smaller bit-width by truncating the number and adding a 1 to the number, if appropriate. also, the architecture of the flex logic cells allows the round function to add the rounded number to another number without increasing logic usage. function prototype the altera hardware description language (ahdl) function prototype for the round function is shown below: function round (dataa[(widthi?)..0], datab[(widthr?)..0] with (widthi, representation, widthr) returns (result[(widthr?)..0], cout, overflow); parameters table 1 shows the parameters for the round function. ports table 2 shows the ports for the round function. table 1. round parameters name value description widthi integers only width of input data representation "signed" "unsigned" sign of the input data. the default value is "unsigned" widthr integers only width of output data (< widthi ) table 2. round ports name type description dataa[(widthi?)..0] input input data datab[(widthr?)..0] input sum data result[(width?)..0] output rounded output data cout output carry out overflow output overflow
altera corporation 3 fs 5 : r ound dat a w o r d rounder functional description the round function implements a data word rounder that provides parameterized input and output widths. the round function rounds a widthi -bit number down to a widthr -bit number, where widthi is the input width and widthr is the output width. the round function can also add the rounded result to another widthr - bit-wide number without increasing logic usage. the round function performs the following calculation: result[(widthr?)..0] = dataa[(widthi?)..(widthi-widthr)] + dataa[widthi-widthr?] + datab[] for example, if the number being rounded is 00101.011 b , the number is rounded down to 00101 b because the fractional part of the number (i.e., the bits to the right of the binary point) is less than 0.5 (0.100 b ). when the bit directly to the right of the binary point is 1, a 1 is added to the result because the fractional part of the number is greater than 0.5 (0.100 b ). figure 2 is a simplified illustration of an 8-bit color channel in a digital video system. in this example, color space conversion is performed using the ycrcb2rgb function. depending on the input values to the ycrcb2rgb function, the multiplication used in the color conversion may result in a 17-bit data word that rolls over. to avoid data word roll over, this 17-bit digital video signal is fed to the saturate function, where it is saturated to a 16-bit word. the signal is then fed to the round function, where it is rounded to an 8-bit word. at this point, the data word is ready for conversion to an analog video signal. figure 2. digital video channel f for information on saturation, refer to functional specification 6 (saturate data word saturator) . for information on color space conversion, refer to rgb2ycrcb & ycrcb2rgb color space converters data sheet . analog v ideo signa l d/a converter round function saturate function ycrcb2rgb function 17 8 8 8 16 8 y cr cb
altera, max, max+plus, max+plus ii, flex, flex 10k, and flex 8000 are trademarks and/or service marks of altera corporation in the united states and other countries. altera acknowledges the trademarks of other organizations for their respective products or services mentioned in this document, specifically: cypress is a trademark of cypress semiconductor corporation. altera products are protected under numerous u.s. and foreign patents and pending applications, maskwork rights, and copyrights. altera warrants performance of its semiconductor products to current specifications in accordance with altera? standard warranty, but reserves the right to make changes to any products and services at any time without notice. altera assumes no responsibility or liability arising out of the application or use of any information, product, or service described herein except as expressly agreed to in writing by altera corporation. altera customers are advised to obtain the latest version of device specifications before relying on any published information and before placing orders for products or services. copyright 1997 altera corporation. all rights reserved. 2610 orchard parkway san jose, ca 95134-2020 (408) 894-7000 http://www.altera.com applications hotline: (800) 800-epld customer marketing: (408) 894-7104 literature services: (888) 3-altera lit_req@altera.com fs 5: round data word rounder 4 altera corporation printed on recycled paper.
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