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SwitchDesign

# SwitchDesign - Draft Draft Draft Designing Computer Systems...

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Draft Draft Draft Designing Computer Systems Switches and Wire 01:30:08 PM 6 February 2010 SW-1 © Scott & Linda Wills

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Draft Draft Draft Designing Computer Systems Switches and Wire Despite their apparent complexity, digital computers are built from simple elements, namely switches and wire . To see how switches and wire can perform computations, consider the circuit below. The battery on the left is connected to the bulb on the right through the switch labeled A . A The battery will light the bulb if there is a complete path for current to flow from one side of the battery to the other. If the switch is open, no current can flow so the light is off. If the switch is closed, current flows and the light is on. The behavior of this simple circuit can be expressed using a table. switch light open off closed on This type of table has been given the lofty name Truth Table . A more meaningful name would be behavior table since it describes the behavior of the circuit. Truth tables list all possible inputs to a system on the left and resulting outputs on the right. A truth table specifies how a system should behave. It does not specify how it should be implemented; this can be done in many ways. Sometimes an icon is used to show connected nodes without drawing a wire. In the circuit below, the triangular symbols below the battery and bulb represent ground . We can imagine that all points attached to ground icons are connected together. So this circuit behaves identically to the circuit above. 01:30:08 PM 6 February 2010 SW-2 © Scott & Linda Wills
Draft Draft Draft A Here’s a system with two switches in series. A B Because each switch can be in one of two states (open or closed) and there are two switches, the truth table has four rows. It’s not so important how we list the input combinations so long as all cases are included exactly once. switch A switch B light open open off closed open off open closed off closed closed on In this circuit, the light is on when switch A is closed AND switch B is closed. This illustrates an important point; series switches produce AND behavior . Using words like open/closed and on/off to describe system behavior is verbose. We can assign the value 0 to an open switch and 1 to a closed switch. Further we can assign the value 0 to an off (dark) bulb and 1 to an on (lit) bulb. Sometimes we’ll refer to 1 as true and 0 as false . Now the truth table becomes more compact. A B Out 0 0 0 1 0 0 0 1 0 1 1 1 The next system has two switches in parallel. 01:30:08 PM 6 February 2010 SW-3 © Scott & Linda Wills

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Draft Draft Draft A B Here the output is true if switch A is closed OR switch B is closed. This illustrates another important point; parallel switches produce OR behavior . Here’s the truth table. A
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SwitchDesign - Draft Draft Draft Designing Computer Systems...

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