Number Systems and Combinational Logic Circuits computer science homework help

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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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