Number Systems and Combinational Logic Circuits computer science homework help

NOTE: Where the solution requires a process, show that process, not simply the solution. Your grade in all the homework assignments and exams depends on the legibility of submission typing or screen shots preferred, ensuring that page arrangement is all the same direction orientation.

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  1.  Convert the following between specified bases:

a) Decimal 496.5625 to: (i) Binary, (ii) Octal & (iii) Hex

b) Binary 11010100.011 to: (i) Decimal, (ii) Octal & (iii) Hex

c) Octal 765.3 to: (i) Decimal, (ii) Binary & (iii) Hex

d) Hex C2F5.B: (i) Decimal, (ii) Binary & (iii) Octal

2.Perform the indicated operations:

a) Division (Binary): 1010110 / 101 (Operation uses multiplications and subtractions: obtain

quotient and remainder, showing your operations step by step.)

b) Multiplication (Binary): 1010 x 1100 (Show steps and result.)

c) Display and Logic (BCD): 0100 1000 0110 0011

 (i) What decimal number does this represent

 (ii) Develop a 10-row logic table to illuminate any decimal number on a 7-segment LED

{segments lettered a – g, from top-to-bottom, left-to-right}. An example the segments

illuminating a 7, 0111, would be 0 1 1 1 (left side for I3 – I0) and 1 0 1 0 0 1 0 (right side for

segments a – g). This reinforces what you’ve done in Lab 1.

3. Using a 4-variable Karnough map, optimize the following functions and show

the resulting function expressed in (i) algebra and (ii) using a logic composed of AND, OR, and

NOT primitives:

a) F(A, B, C, D) = Σm(0, 2, 4, 5, 8, 10, 11, 15)

b) F(A, B, C, D) = Σm(0, 1, 2, 4, 5, 6, 10, 11)

c) F(W, X, Y, Z) = Σm(0, 2, 4, 7, 8, 10, 12, 13)

4. Don’t Care. Using a Karnough map and specified don’t-care conditions d,

optimize the following functions and show the resulting function expressed in (i) algebra and

(ii) using a logic composed of AND, OR, and NOT primitives:

a) F(A, B, C) = Σm(3, 5, 6), d(A, B, C) = m(0, 7)

b) F(W, X, Y, Z) = Σm(0, 2, 4, 5, 8, 14, 15), d(W, X, Y, Z C) = Σm(7, 10, 13)

c) F(A, B, C, D) = Σm(4, 6, 7, 8, 12, 15), d(A, B, C, D) = Σm(2, 3, 5, 10, 11, 14)

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