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20085eeM16_2_Fall08_Homework4_Soln

# 20085eeM16_2_Fall08_Homework4_Soln - UCLA Department of...

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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). 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?

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(a) SoP: X0.X1.X3’ + X0.X1’.X2.X4’ + X1.X2’.X3’.X4’ + X0.X1.X2’.X4’ + X0.X2’.X3’.X4 + X0.X2.X3.X4 (b) PoS: (X0+X1) (X0+X3’) (X0+X4’) (X1+X2+X3’) (X0+X1’+X2’)
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20085eeM16_2_Fall08_Homework4_Soln - UCLA Department of...

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