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d07hwk3sol - f h 5 ECE2022 HWK 3/— D07 Homework is due...

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Unformatted text preview: f ) / h 5 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 = (a3, a2, a1, do) where (10 is the least significant 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 2 0. (3) Give the truth table for F as a function of a3, a2, a1, a0. \4 o 0 0 o 7) 0 D 0 t l l J l l l l (b) Write out the canonical sum of minterms expression for F. .— —- f0: 613474121; + 434;“.00'4‘2342‘33404 434,161,30 +9525”; 1- + GJQL4,49 +QJZquQo {-Q] at 3'30 +afqzqi§0+ “fizqflo (c) Obtain a simplified expression for F using a Karnaugh Map. (Be sure to show the Karnaugh map and the prime implicants (rectanges) you have selected for the simplification on your homework sheet.) Be careful, this is a tricky one, make sure you choose essential prime implicants first! (e) Draw the circuit diagram, that implements F. Problem 2 - 40 points total For each of the following truth tables, use a Karnaugh map to produce a simplified sum of products expression. The X’s in the tables indicate “don’t cares”. Be sure to show your Karnaugh map with clearly circled groups that correspond to your Sum of Products solution. Please draw your final Karnaugh maps, clearly labelled and the resulting simplified logic expressions next to them on the next two blank sheets. (a) Three Variable Map x Y z A 0 0 0 1 Q 00 (9‘ H ‘O 0 01 0 w! 010 1 011 1 100 1 101 0 1 10 1 111 1 (c) Three Variable Map X A Y Z 01010110 00110011 00001111 Problem 3 — 30 points total For the function given; F : (A+C)(A'+B)+B’C+BC’+BC (3) Produce a truth table that expresses F as a function of A, B, and C. _ A g c (Mo (A’+ 1:3 s'o a) no P 0 O o o I O 0 O 0 o o \ l I " 0) o l O \ O 0. I 0 l: 0 ( o) M {“ng “Lam W 90m A...“ t ' a 0 1 0 0 0 0 C9 l 0 l l 0 l 0 0 l I Q 0 l l 0 q 0 I l l l l l b o \ a (b) Use a Karnaugh map to produce a simplified sum of products form. (Show both the Karnaugh map and Sum of Product expression) A{00& &\ \\ lo (c) Draw the circuit diagram for an implementation from your simplified sum of products expression using just AND Gates and OR gates (assumming as usual ’that you have access to each literal and its logical inversion). (d) Draw the circuit diagram of a NAND gate only implementation from your simplified sum of products expression. ‘9‘ F’cc~ ED ’le P“; Q Dom—{joflrd afL Z 5&5 o 6’ 0" r- (9) Use a Karnaugh map to produce a simplified product of sums form. (Show both the Karnaugh map and simplified expression) F = (Em) (f) Draw the circuit diagram for an implementation from your simplified product of sums expression using just AND Gates and OR gates (assumming as usual that you have access to each literal and its logical inversion). ASW’ ...
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