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CHAP_2_SOLUTIONS_SET_1

CHAP_2_SOLUTIONS_SET_1 - EE 311 Digital Hardware...

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EE 311 Digital Hardware Organization Chapter 2 Homework Solutions (Set 1) 2.1. The proof is as follows: (x + y)(x + z) = xx + xz + xy + yz = x + xz + xy + yz = x(1 + z + y) + yz = x(1) + yz = x + yz 2.2. The proof is as follows: (x + y)(x + y ) = xx + xy + xy + yy = x + xy + xy + 0 = x(1 + y + y) = x(1) = x 2.3. Manipulate the left hand side as follows: xy + yz + xz = xy + (x + x)yz + xz = xy + xyz + xyz + xz = xy(1 + z) + xz(y + 1) = xy(1) + x(1)z = xy + xz 2.4. Proof using Venn diagrams:
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