The number of switching elements achievable in the final answer is given for

The number of switching elements achievable in the

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The number of switching elements achievable in the final answer is given for you. (a) This circuit can be simplified down to 6 switching elements. (Note that 4 of the switching elements shown are for negated variables.) a X X X’ Y W S Z Z’ V b Z’ V Z W S’ Z Y V (b) This circuit can be simplified down to 6 switching elements. (Note that 4 of the switching elements shown are for negated variables.) b S Y X Y’ V W S Z Y S Y Z’ X’ S V a X’ Y S W (c) This circuit can be simplified down to 9 switching elements. (Note that 7 of the switching elements shown are for negated variables.) Y X Y W S V V V Z W S X S X S Y W Y a Z S V S b V Z Z Y X X X V
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EE 5393, Winter ’13 3 (d) This circuit can be simplified down to 8 switching elements (7 for extra credit). (Note that 9 of the switching elements shown are for negated variables.) a Z X Z Y X’ Z V Y’ X S V’ b V’ S Y’ S Y V’ S Y Y’ Z’ X Z S Y X Y Y S’ Y V W S S
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EE 5393, Winter ’13 4 2. Two-Terminal Switches, but Multiple Circuit Terminals (no collabora- tion) A generalization of the switching circuit model is a circuit with multiple circuit terminals. A function F ab is 1 if there is a closed path between terminals a and b , and 0 otherwise. With multiple circuit terminals, a, b, c, d, . . . , different functions can be implement between pairs of terminals. For instance, for the circuit x y' z a b e c x' y d f we have F af = xyz F bd = x 0 z F cf = 0 . and so on. For the circuit w x y z a b c we have F ab = x + w F bc = y + z F ac = ( x + w )( y + z ) . As these examples show, you can use either a variable or its complement to control a switch. (Each terminal is, in fact, any stretch of wire.)
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EE 5393, Winter ’13 5 (a) Construct a circuit with 3 switches that implements the functions f 1 = xy f 2 = x 0 y (b) Construct a circuit with 4 switches that implements the functions f 1 = xy + x 0 y 0 f 2 = x 0 y + xy 0 (c) Construct a circuit with 6 switches that implements the functions f 1 = x ( y + z ) f 2 = y ( x + z ) f 3 = z ( x + y ) f 4 = x + yz f 5 = y + xz f 6 = z + xy (d) Construct a circuit with as few switches as possible that implements all functions of two variables. A solution with 8 switches gets full credit.
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