What is the difference between fixed and floating point numbers

Since the gaps between adjacent numbers can be much larger with fixed-point processing when compared to floating-point processing, round-off error can be much more pronounced. As such, floating-point processing yields much greater precision than fixed-point processing, distinguishing floating-point processors as the ideal DSP when computational accuracy is a critical requirement. Dynamic range and precision considerations typically define the criteria used by designers to determine whether fixed-point or floating-point processors are ideally suited for an application — where computational demands are high, floating point is favored.

But there are many other important interrelated factors to consider when choosing between the two formats. Fixed-point DSPs are used in a greater number of high volume applications than floating-point DSPs, and therefore are typically less expensive that floating-point DSPs due to the scale of manufacturing.

System- on-a-chip SOC variables, including on-board memory, integrated application-specific peripherals, and connectivity options can also affect the cost - and functionality - of both fixed-point and floating-point processors. Ease of development : The easier it is for a designer to develop a product, the more likely it is that the product can be brought to market ahead of the competition. It is generally easier to develop algorithms for floating-point DSPs, as fixed point-algorithms require greater manipulation to compensate for quantization noise.

As such, designers typically choose floating-point DSPs when implementing complex algorithms. Here again, SOC variables can shorten product development cycles, as can the ecosystem of associated product development tools and third-party support software. In general, floating point math offers a wider range of numbers and more precision than fixed point math.

Knowing the difference, and when to use which type of math can make a difference in terms of a faster calculation or a more precise calculation. Mostly, the objective is to use only as much calculating power as you will need to get the job done. A fundamental difference between the two is the location of the decimal point: fixed point numbers have a decimal in a fixed position and floating-point numbers have a sign. Referring to Figure 1, fixed point numbers have a certain number of reserved digits that are on the left side of the decimal for the integer portion of the number.

The numbers to the right of the decimal point are reserved for the fractional part of the number. If your MCU only uses fixed numbers, the decimal stays in the same place in that if two digits are set for the fractional portion, then that is the level of precision you will have going forward. Very large numbers and very small numbers will have to fit in the same number of placeholders, what is actually bits, separated by the decimal in the same place, regardless of the number.

For instance, if a fixed-point format will represent money, the level of precision might be just two places after the decimal. The programmer, knowing the register need hold only two bits after the decimal point, can put in and know that the fixed-point unit will interpret that number as There are three parts of a fixed-point number representation: the sign field, integer field, and fractional field. The advantage of using a fixed-point representation is performance and disadvantage is relatively limited range of values that they can represent.

So, it is usually inadequate for numerical analysis as it does not allow enough numbers and accuracy. A number whose representation exceeds 32 bits would have to be stored inexactly. These are above smallest positive number and largest positive number which can be store in bit representation as given above format. This representation does not reserve a specific number of bits for the integer part or the fractional part. Instead it reserves a certain number of bits for the number called the mantissa or significand and a certain number of bits to say where within that number the decimal place sits called the exponent.

The floating number representation of a number has two part: the first part represents a signed fixed point number called mantissa. In fixed point representation, the number of digits before and after the radix cannot be changed. Considering two digits in front of the radix and two digits after the radix, the minimum number that can be represented is In this scenario, a number such as As an alternative, the number can be represented as This is called precision reduction. It is not the actual value, just an approximation.

Overall, fixed point representation allows improving the performance. On the other hand, it can only be used to represent a limited range of values. Floating point representation can be used to overcome the limitations of fixed point representation. Therefore, most modern computers use floating point representation to store fractional numbers in memory. It can represent very large and very small numbers precisely.