Functional Specification - Altera Corporation

Altera Corporation 1

round

Data Word Rounder

February 1997, ver. 1 Functional Speciﬁcation 5

A-FS-05-01

Features

■

round reference design implementing a data word rounder

■

Parameterized input and output widths

■

Optimized for FLEX

10K and FLEX 8000 device families

■

Rounds arbitrary-length words to shorter words

■

Signed (two's complement) or unsigned operation

■

Built-in post-round adder

■

Supported by MAX+PLUS

■

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

) yields 1 (01

), and rounding

the decimal number 1.75 (01.11

) yields 2 (10

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–1)..0],

datab[(WIDTHR–1)..0]

WITH (WIDTHI, REPRESENTATION, WIDTHR)

RETURNS (result[(WIDTHR–1)..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

"UNSIGNED"

WIDTHR

Integers only Width of output data (<

WIDTHI

)

Table 2. round Ports

Name Type Description

dataa[(WIDTHI–1)..0]

Input Input data

datab[(WIDTHR–1)..0]

Input Sum data

result[(WIDTH–1)..0]

Output Rounded output data

cout

Output Carry out

overflow

Output Overflow

Altera Corporation 3

FS 5: round Data Word 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

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–1)..0]

dataa[(WIDTHI–1)..(WIDTHI-WIDTHR)]

dataa[WIDTHI-WIDTHR–1]

datab[]

For example, if the number being rounded is 00101.011

, the number is

rounded down to 00101

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

). 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

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

For information on saturation, refer to

Functional Specification 4 (saturate

Data Word Saturator)

. For information on color space conversion, refer to

RGB2YCrCb & YCrCb2RGB Color Space Converters Data Sheet

Analog

Video

Signal

D/A

Converter

Round

Function

Saturate

Function

YCrCb2RGB

Function 17

16 8

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

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is a trademark of Cypress Semiconductor Corporation. Altera products are protected under numerous U.S.

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of its semiconductor products to current specifications in accordance with Altera’s 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.

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FS 5: round Data Word Rounder

4 Altera Corporation

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