I2 Iterative Design - The Comparator

# I2 Iterative Design - The Comparator - Iterative Design: A...

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Iterative Design: A Design Example First, it is worth reviewing the points made in the document Iterative Design: A First Approach as to when it is appropriate or inappropriate to embark upon an iterative design for some system: Iterative design works when the all of the equations in a set of equations operate in the same fashion , or in some fashion that corresponds to their position in a set of equations . The only real difference in each equation is the position of the output in the set. Further, we are assuming that each equation depends on a well-defined subset of the input set – each one in the same fashion Based on these assumptions, we hypothesize that if we can complete the design of a general equation describing one arbitrary output , we can then iterate that equation over the range of precision required by the output set, considering boundary conditions where appropriate. Begin by trying to form the equation for some arbitrary state or output . ( y i + , z i , etc.) Look for an input or inputs that partition the operation of the equation into distinct (and perhaps mutually exclusive) modes. In [the shift register], the mode select inputs determine what the circuit does for any combination of that pair of inputs. Since one of the four combinations of S 1 and S 0 is always present, designing the circuit amounts to determining what the output does for each combination of S 1 and S 0 . After you have fully derived the general equation, iterate the equation for each valid value of i . Check each equation for a boundary problem ; boundary problems exist when iterating the general equation requires a bit that doesn’t exist. Solving the boundary problem amounts to establishing a boundary question that accounts for the undefined bit in a manner that is consistent with the specification. Just as it is in the process of deriving the general equation, establishing boundary conditions is a matter of studying the specification and understanding the behavior of the circuit. The design problem is that it isn’t always easy to find the way in which a specification satisfies the assumptions that allow us to apply the hypothesis described above. Here is one such design example: Specification A comparator circuit takes in two n -bit inputs called A (which consists of A n – 1 A n – 2 …A 1 A 0 ) and B (which consists of B n – 1 B n – 2 …B 1 B 0 ) and provides three outputs, G, E, and L. If A and B are taken to represent unsigned binary numbers , the three mutually-exclusive outputs operate as follows: G = 1 if and only if A > B L = 1 if and only if A < B E = 1 if and only if A = B Implement the comparator circuit using an iterative design. The Iterative Design Principle

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## This note was uploaded on 01/17/2011 for the course ECE 3504 at Virginia Tech.

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I2 Iterative Design - The Comparator - Iterative Design: A...

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