Ecen 248 HW2

Ecen 248 HW2 - = a + ab + bc + ac + bcd = a + ab + ac + bc...

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EE 248: Assignment #2 1. Prove DeMorgan’s law, written in the form ( x 1 + x 2)’ = x 1’ x 2’ 2. Consider the circuit Function g in the diagram (a) Transform the circuit by removing the XOR gates and replacing them by AND, OR and INV gates.
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(b) Now transform the resulting circuit from the previous part into one which only uses OR, NOR and INV gates. 3. Prove the equivalence of the two logical expressions given below: a + bc = (a + b)(a + c) + ac + bcd = a(a + c) + b(a + c) + ac + bcd = aa + ac + ab + bc + ac + bcd
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= a + ac + ab + bc + ac + bcd = a(1 + c) + ab + bc + ac + bcd
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Unformatted text preview: = a + ab + bc + ac + bcd = a + ab + ac + bc + bcd = a(1 + b + c) + bc(1 + d) = a + bc 4. a) Algebraically reduce the function f = (ab+cd)(abd + bc)(c + bcd) + b. Show step by step work. f = (ab + abcd)(c + bcd) + b = (abc + abcd ) + b = abc + b fr= ac + b b) Show using a truth table for f and f* (reduced f) that the f* is equivalent to the original f abcd f fr 0000 0 0 0001 0 0 0010 0 0 0011 0 0 0100 1 1 0101 1 1 0110 1 1 0111 1 1 1000 1 1 1001 1 1 1010 0 0 1011 0 0 1100 1 1 1101 1 1 1110 1 1 1111 1 1...
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Ecen 248 HW2 - = a + ab + bc + ac + bcd = a + ab + ac + bc...

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