20085eeM16_2_Homework4 - d Draw a circuit to implement this...

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UCLA Department of Electrical Engineering EEM16 Homework 4 Due November 4 th , 2008 1. You are designing a combinational system whose input is an integer X in the range [0, 31] represented a bit-vector of 5 bits <X 4 , X 3 , X 2 , X 1 , X 0 >, and whose output P takes the value 1 if X is a prime number, and is 0 otherwise. a. Write the switching expression for P in a sum-of-products form. b. Write the switching expression for P in a product-of-sums form. c. Using the identities of Boolean Algebra, show that the two expressions in parts (a) and (b) are equivalent (i.e. convert one to another).
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Unformatted text preview: d. Draw a circuit to implement this combinational system using only 2-input NOR gates. e. How many transistors would this circuit require were it to be implemented in CMOS? 2. Reverse engineer the circuit shown in the schematic of Figure 1 in order to derive a two-level realization. a. Find the Boolean expression that describes the circuit. b. Construct the truth table for the function. c. Write the function in sum-of-products form. d. Simplify the function using K-maps. Figure 1 3. Exercise 5.18 4. Exercise 6.4 5. Exercise 6.6...
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