Numerical Precision Assignment Example | Topics and Well Written Essays - 1000 words

Numerical Precision - Assignment Example32 blots. Floating token total pool is composed of two components that is, the mantissa and the exponent. The exponent consists of eight bits value which ranges from zero to 255. On the another(prenominal) hand, the mantissa is twenty four bit long with 1 being its most significant bit which is usually never stored. Also, there is a sign bit (+ and -) which is used to indicate whether the number is cast out or positive Floating story add up in arithmetic calculations Floating point numbers calculations vary from machine to machine depending on the precision of the machine. Precision is the degree of correctness a attached quantity can be denotative this includes 32-bit single precision and 64-bit double precision that be stored as 8 and 10 bytes respectively. This representation makes it very easy for hardware manipulation. Assignment of these values doesnt take the knowledge of how the various numbers are stored in memory. For calc ulation purposes, this requires the pulling of individual parts of the numbers involved and manipulating them accordingly. Floating point used in arithmetic computations are easy to work with since they are expressed to base 2 and the exponent is a decimal value that can be expressed as binary within the computer. The fixed number notation of representing floating point numbers may lead to loss of precision such as expressing results in form of 32 bits and they may be greater than 32 bits. Floating point arithmetic is slow and therefore less efficient compared to whole number arithmetic. Also, floating point arithmetic is less true due to round off errors. Floating point stage is not memory efficient at all. This is because the results of computation entrust require additional shop in memory which may be limited. This is usually the case with majority of computers especially personal computers and its therefore advisable to let dedicated devices to perform floating point compu tations. Binary Coded Decimal format This format is a format for representing decimal numbers such that severally number is represented by a number of bits (four or eight bits).There is the packed and unpacked varied binary coded decimal formats. In the packed format, each decimal number is represented using 4 bits (nibble) while in the unpacked format each decimal is represented using a byte (8 bits). For example to represent a number like 41 in binary coded decimal format entrust be Packed format 0100 0001 and the unpacked format will be 0000 0100 0001 The packed BCD format is more memory efficient since it reduces on the number of unused bits added to a number. Comparison of the BCD format to the floating point format Precision BCD values are very accurate as compared to floating point numbers. This is because BCD numbers are simply decimal numbers expressed in terms of bits and floating point number format is a scientific notation of large and teeny values. Performance in ca lculations BCD numbers are easy to convert and use in arithmetic hence the overall arithmetic computation is always very fast and efficient. Floating point format numbers must undergo various steps of con indication before they can be used in any computation. These results in some overhead in terms of memory and time hence the computations will be slow. Memory Usage BCD format is efficient in memory usage if the packed version is used. The unpacked version results