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Write an implementation for the Prime machine (de?ned at the end of the assignment sheet). Provide a suitable invariant and variant for any loop you use. Provide comments in your machine stating the precondition and postcondition which the initialised loop meets.
An abstract machine, Bu?er is de?ned at the end of this assignment sheet. Provide a re?nement of this machine which stores the queue in an array:
aa : 1 . . qlen → ELEM
When elements are removed from the front of the queue, the array itself is not altered but the positions become available for overwriting. When adding elements, once the end of aa is reached, wrap-around can occur if positions at the front of aa are available. Thus forexample, if the capacity is 8, the sequence [a, b, c, d] may correspond to:
etc (where * indicates any element).
To do this you will need to introduce some further state variables to keep track of the situation in the array and to enable you to relate the state of aa to the state of bu? . Provide the linking invariant which captures this invariant and incorporate it in a re?nement machine BufferR.
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Design an OR to AND gates combinational network and NAND only n/w for the following Boolean expression: A'BC'D + ABC'D' + A'B'CD' + A'BCD'
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Write a function that will get a variable number of input arguments: the length and width of a rectangle, and possibly also the height of a box that has this rectangle as its base.
The address bus is unidirectional due to the address information is always given by the Micro Processor to address a memory location of an input or output devices.
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