d07hwk3

d07hwk3 - ECE2022 Homework is due Tuesday April 3 2006...

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ECE2022 HWK 3 D07 Homework is due Tuesday April 3, 2006. Problem 1 – 30 points We will design part of a set of logic circuits that tests numbers for divisbility for certain prime numbers as part of an information encryption system. The binary number A is represented by a four bit unsigned number: A = ( a 3 , a 2 , a 1 , a 0 ) where a 0 is the least signiFcant bit, etc. The circuit you must design will have a single output, F , which must take on the value of 1 if A is divisible by 2 or 3 and zero otherwise, except when A = 0 (which is “technically” divisible by any number) for which case we want F = 0. (a) Give the truth table for F as a function of a 3 , a 2 , a 1 , a 0 . (b) Write out the canonical sum of minterms expression for F . f 0 = 1
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Obtain a simplifed expression For F using a Karnaugh Map. (Be sure to show the Karnaugh map and the prime implicants (rectanges) you have selected For the simplifcation on your homework sheet.) Be careFul, this is a tricky one, make sure you choose essential prime implicants frst! F
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d07hwk3 - ECE2022 Homework is due Tuesday April 3 2006...

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