Bit Serial Arithmetic In Dsp

13.5 BIT-SERIAL FILTER DESIGN AND IMPLEMENTATION FIR and IIR filters are the two most basic structures used in DSP. This section considers design of bit-serial FIR and IIR digital filters with fixed constant coefficients, where the multiplications with constant coefficients are decomposed and implemented using bit-serial shifts and adds. 13.5.1 Bit-Serial FIR Filter Consider the implementation of the FIR filter with a signal wordlength of 8. Equation () can be rewritten in terms of shifts and adds as follows: The word-level signal flow graph of the shift-add based FIR filter is shown in (a). Due to the presence of noncausal scaling operators, this is not a feasible design.

Pipelining cutsets, shown in dashed lines in (a), can be used to delay the advance scaling operations. By placing delay elements along the cutsets and replacing the delayed scaling operators with switches, a feasible bit-level pipelined bit-serial FIR filter can be derived, as shown in (b). Note that a word-level delay is equivalent to W bit-level delays for a signal wordlength of W.

Nov 23, 2010 - We describe a pseudo floating point bit serial circuit which is less complex than. Arithmetic for performing mathematical operations for signal.

Therefore, the one word delay in (a) is replaced by 8 bit-level delays in (b). The switching time instances can be derived by scheduling the bit-level computations. With Safari, you learn the way you learn best.

Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Many and require the serialization or enumeration of related entities. For example, a must know whether some packet comes 'before' or 'after' some other packet. The () attempts to define 'Serial Number Arithmetic' for the purposes of manipulating and comparing these. This task is rather more complex than it might first appear, because most algorithms use fixed size () representations for sequence numbers.

Emilio pujol guitar school pdf files free. It is often important for the algorithm not to 'break down' when the numbers become so large that they are incremented one last time and 'wrap' around their maximum numeric ranges (go instantly from a large positive number to 0, or a large negative number). Unfortunately, some protocols choose to ignore these issues, and simply use very large integers for their counters, in the hope that the program will be replaced (or they will retire), before the problem occurs (see ). Many communication protocols apply serial number arithmetic to packet sequence numbers in their implementation of a. Some versions of TCP use.

PAWS applies the same serial number arithmetic to packet timestamps, using the timestamp as an extension of the high-order bits of the sequence number. Contents • • • • • • • • Operations on sequence numbers [ ] Only addition of a small positive to a sequence number, and comparison of two sequence numbers are discussed. Descargar torrent volver almodovar. Only unsigned binary implementations are discussed, with an arbitrary size in bits noted throughout the RFC (and below) as 'SERIAL_BITS'.

Addition [ ] Adding an integer to a sequence number is simple unsigned integer addition, followed by unsigned to bring the result back into range (usually implicit in the unsigned addition, on most architectures.) s' = (s + n) modulo (2 ^ SERIAL_BITS) Addition of a value outside the range [0. (2 ^(SERIAL_BITS - 1) - 1)] is undefined. Basically, adding values beyond this range will cause the resultant sequence number to 'wrap', and (often) result in a number that is considered 'less than' the original sequence number! Comparison [ ] A means of comparing two sequence numbers i1 and i2 (the unsigned integer representations of sequence numbers s1 and s2) is presented. Equality is defined as simple numeric equality.

The algorithm presented for comparison is very complex, having to take into account whether the first sequence number is close to the 'end' of its range of values, and thus a smaller 'wrapped' number may actually be considered 'greater' than the first sequence number. Thus i1 is considered less than i2, only if: (i1 i2 and i1 - i2 > 2^(SERIAL_BITS - 1)) Likewise, i1 is considered greater than i2, only if: (i1 2^(SERIAL_BITS - 1)) or (i1 > i2 and i1 - i2 (s2 + 1) which is just as non-intuitive. Thus the problem case is left undefined, implementations are free to return either result, or to flag an error, and users must take care not to depend on any particular outcome. Usually this will mean avoiding allowing those particular pairs of numbers to co-exist. Thus, it is often difficult or impossible to avoid all 'undefined' comparisons of sequence numbers. However, a relatively simple solution is available. By mapping the unsigned sequence numbers onto signed arithmetic operations, every comparison of any sequence number is defined, and the comparison operation itself is dramatically simplified.