Project Report free essay sample

The implementation of encoder-decoder involved conversion of the Fixed point number to Standard Logic vector. After the encoding and decoding process the Slandered Logic vector is converted back to Fixed point number then back to Real Number representation. Quantization error is calculated form the difference between input and output real numbers. We have utilized Xilinx ISE simulator and IEEE proposed Fixed Point package during execution of the projects. Figure 1 shows the block diagram representation of the proposed system. INPUT (Type: Real) Sample Values Real To Fixed Point Conversion Signed Quantization Level (3 downto -4) Resolution (0. 0625) Fixed Point to IEEE Standard Bit Vector Conversion Hex Encoding Binary to Octal Encoding / Encryption Hex Encoding Octal to Binary Decoding / Decryption Hex Encoding IEEE Standard Bit Vector to Fixed Point Conversion Fixed Point To Conversion Real Type Conversion Conversion Error Calculation Figure 1: Block Diagram of Complete Simulation Model 1. 1 Fixed Point Package : Fixed point is a step between integer math and floating point. We will write a custom essay sample on Project Report or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page This has the advantage of being almost as fast as numeric_std arithmetic, but able to represent numbers that are less than 1. 0. A fixed-point number has an assigned width and an assigned location for the decimal point. As long as the number is big enough to provide enough precision, fixed point is fine for most DSP applications. Because it is based on integer math, it is extremely efficient, as long as the data does not vary too much in magnitude. This package defines two new types: â€Å"ufixed† is the unsigned fixed point, and â€Å"sfixed† is the signed fixed point. 1. 2 IEEE floating-point representations of real numbers No human system of numeration can give a unique representation to every real number; there are just too many of them. So it is conventional to use approximations. For instance, the assertion that pi is 3. 14159 is, strictly speaking, false, since pi is actually slightly larger than 3. 14159; but in practice we sometimes use 3. 14159 in calculations involving pi because it is a good enough approximation of pi. One approach to representing real numbers, then, is to specify some tolerance epsilon and to say that a real number x can be approximated by any number in the range from x epsilon to x + epsilon. Then, if a system of numeration can represent selected numbers that are never more than twice epsilon apart, every real number has a representable approximation. For instance, in the United States, the prices of stocks are given in dollars and eighths of a dollar, and rounded to the nearest eighth of a dollar; this corresponds to a tolerance of one-sixteenth of a dollar. In retail commerce, however, the conventional tolerance is half a cent; that is, prices are rounded to the nearest cent. In this case, we can represent a sum of money as an whole number of cents, or equivalently as a number of dollars that is specified to two decimal places. Scientists and engineers long ago learned to cope with this problem by using scientific notation, in which a number is expressed as the product of a mantissa and some power of ten. The mantissa is a signed number with an absolute value greater than or equal to one and less than ten. So, for instance, the speed of light in vacuum is 2. 99792458 x 10^8 meters per second, and one can specify only the digits about which one is completely confident. Using scientific notation, one can easily see both that 1. x 10^-2 is more than twice as large as 6 x 10^-3, and that both are close to 1 x 10^-2; and one can easily distinguish 4 x 10^-3 and -7 x 10^-4 as small numbers of opposite sign. The rules for calculating with scientific-notation numerals are a little more complicated, but the benefits are enormous. The three things that vary in scientific notation are the sign and the absolute value of the mantissa and the exponent on the power of ten. A system of numeration for real numbers that is adapted to computers will typically store the same three data a sign, a mantissa, and an exponent into an allocated region of storage. By contrast with fixed-point representations, these computer analogues of scientific notation are described as floating-point representations. The exponent does not always indicate a power of ten; sometimes powers of sixteen are used instead, or, most commonly of all, powers of two. The numerals will be somewhat different depending how this choice is made. For instance, the real number -0. 125 will be expressed as -1. 25 x 10^-1 if powers of ten are used, or as -2 x 16^-1 if powers of sixteen are used, or as -1 x 2^-3 if powers of two are used. The absolute value of the mantissa is, however, always greater than or equal to 1 and less than the base of numeration. The particular system used on MathLAN computers was formulated and recommended as a standard by the Institute of Electrical and Electronics Engineers and is the most commonly used numeration system for computer representation of real numbers. Actually, their standard includes several variants of the system, depending on how much storage is available for a real number. Well discuss two of these variants, both of which use binary numeration and powers of 2: the IEEE single-precision representation, which fits in thirty-two bits, and the IEEE double-precision representation, which occupies sixty-four bits. Well begin with single-precision numbers, since it is this representation that is used in HP Pascal for values of the Real data type. In the IEEE single-precision representation of a real number, one bit is reserved for the sign, and it is set to 0 for a positive number and to 1 for a negative one. A representation of the exponent is stored in the next eight bits, and the remaining twenty-three bits are occupied by a representation of the mantissa of the number. The exponent, which is a signed integer in the range from -126 to 127, is represented neither as a signed magnitude nor as a twos-complement number, but as a biased value. The idea here is that the integers in the desired range of exponents are first adjusted by adding a fixed bias to each one. The bias is chosen to be large enough to convert every integer in the range into a positive integer, which is then stored as a binary numeral.