floating point

Fixed point (part two)

Fixed point.

Please read this article before you read the below content…

However , Fixed point arithmetic is popular in embedded system or the high performance system but low power consumption (system that desiged with the
limitation in budget).The primary advantage of fixed point system is “in fixed point , the calculation process of rational number is done in the same way as
calculation process of integer number”. So , it has advantage over floating point in that it require only Arithmetic Logic Unit or ALU (ALU is only the
unit that exist in almost CPU in the world) in its computation process. On the contrary , floating point arithmetic require both ALU and FPU (FPU is hardware
processing unit that used for handle the floating point calculation process). Please look at this page for more information about FPU Design.

You may find out some digital signal processing (DSP) chips don’t have the FPU part , that’s not strange because fixed point can be used in DSP tasks too.
The DSP chip without FPU make its cost cheaper, furthermore it consume less energy when compare to DSP chip with FPU.
Blackfin of Analog Devices or TMS320C5x series of Texas Instruments is an example of Fixed-point DSP chip.

Due to the operation speed of Fixed point is faster than floating point, so in some kind of tasks that need to complete calculation process
within the limit of time, in this case Fixed point DSP processor is more applicable than floating point DSP processor.

The efficiency of DSP processor can be measured by “the capability in multiply and accumulate per second”.The official technical word call
it “Millions of Multiply Accumulates (MMAC) per second” or “MMAC per second” or MMACs.
The MMACs value of fixed point DSP processor is higher than floating point DSP processor.
You can easily compare DSP chip from Texus Instruments in these two series , TMS320C67x (Floating point processor)
and TMS320C64x (Fixed point processor) , please click the link under the chip series and you will know that the peak MMACs of TMS320C64x series
is much higher than TMS320C67x.

So , I can summarize that high performance DSP chip mostly use Fixed point arithmetic. Task that suitable for using high MMACs Fixed-point DSP chip
is the task that include heavily mathematical calculation such as Audio Coding or Graphic Engine in video games box etc…

The next article is the last article relate to fixed point. It will about Q-format.

Thank you,
Jitkasem

Reference : Semiconductor Electronics Magazine , Thailand (September/2553 issue).

Fixed point and floating point (part one)

Fixed point.

Numerical system in computer can be separated into 2 group , one is Floating point and another one is Fixed point. Floating point is mainly
used in calculation of software that run on PC. In PC there is the FPU or Floating Point Unit so it is possible to use floating point numerical system.
On the other hand , in embedded system , the capability of main processor is limit and maybe there’s no FPU so in calculation , the usablility of Fixed point
instead of Floating point is necessary.

Fixed point is numerical system that use binary number or bit (0 and 1) to represent an integer , rational number or signed integer (such as -1,-3,-5).
Most people think that fixed point is the system that used for calculated only integer but in fact , it can be used for calculate an integer , rational number and signed integer too.

The difference between Fixed point and Floating point.

First , let me talk about rational number…

Rational number is derive from the representation of ratio of two integer A and B or A/B. You can write rational number in decimal format
such as 12.25 , 1.10 , etc. The symbol between integer part and fractional part is called “decimal point” or “radix point”. Position of radix point in the rational
number can be anywhere depend on the significance of that number.

Fixed point number represent the number that the position of radix point is fixed and not change even though that number is modified by the
computation process.This mean that in Fixed point the number of digits come after the radix point is also fixed too.

Floating point number represent the number that the position of radix point is “floating” (not fixed at any position). The position of radix point
can be changed during number is modified in computation process. Or this mean the number of digits come after the radix point can be varied (not fixed).

From the above information, when compare Floating point with Fixed point , range of number can be represented by floating point is larger than fixed point.
Floating point is suitable in the task that require intensive computation such as Hi-Fi Audio System, Radar System, Medical Electronics system , etc.
General purpose computer is mainly use Floating point too. The popular programming language like C and C++ are also not support the fixed point , however
there’re many existing fixed point math libraries able to use with C and C++. The IEEE Standard for Floating point Arithmetic is IEEE 754 and this standard is
implemented into both hardware (FPU) and software of computer.

In next article (Part two) will be about the advantage of fixed point.

Thank you,

Jitkasem