ECE251 hw8 - sol

ECE251 hw8 - sol - NEW JERSEY INSTITUTE OF TECHNOLOGY DEPT....

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Unformatted text preview: NEW JERSEY INSTITUTE OF TECHNOLOGY DEPT. OF ELECTRICAL & COMPUTER ENGINEERING ACADEMIC YEAR 2008-2009 SEMESTER 1 ECE251 DIGITAL DESIGN S OLUTION HW8 1. A half-adder (HA) with inputs x and y produces the sum bit S 1 and the carry bit C 1 : xy C y x S = ⊕ = 1 1 A full-adder (FA) with carry input C in and inputs a and b produces a sum bit S and a carry out C out given by: ) ( b a C ab C C b a S in out in + + = ⊕ ⊕ = Suppose we take 2 HAs and perform the following connections: HA HA a b C* S* 1 C 1 S in C 2 C Fig. 1 FA implementation using 2 HAs and one OR gate Notice that S S = * , and out C C = * : in C S S ⊕ = 1 * , S C b a S b a S in = ⊕ ⊕ = ⇒ ⊕ = * 1 ) ( ) ( * 1 2 1 b a b a C ab b a C ab C S ab C C C in in in + + = ⊕ + = + = + = in in in in in in bC ab b a C C a a a b b a C C a a b b a C + + = + + + = + + = ) )( ( ) ( 1 out i in in in in in in C b a n C ab bC C b a bC C b b b a bC C b b a = + + = + + = + + + = + + = ) ( ) ( ) )( ( ) ( Therefore, this connection implements an FA.Therefore, this connection implements an FA....
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ECE251 hw8 - sol - NEW JERSEY INSTITUTE OF TECHNOLOGY DEPT....

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