Incremental Encoders • Encoders typically run on +5V, not +24V • Outputs are typ. not 24V compatible either
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Incremental Encoders • Encoders typically run on +5V, not +24V • Outputs are typ. not 24V compatible either
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Incremental Encoders • Encoders typically run on +5V, not +24V • Outputs are typ. not 24V compatible either
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Quadrature Shaft Encoding • Basic shaft encoding method: measures how far an axle rotates and its speed, but cannot tell when the axle changes direction • Quadrature Shaft Encoding: measures precise rotation of axles and velocity; maintains accurate counts even when the axle’s direction of rotation changes • Applications: – Position monitoring of trapped systems, where the mechanics of a system limit travel between known stop positions, e.g., rotary robot arms, where encoders are used to measure joint angles, and Cartesian robots, where the rotation of a long worm screw moves a rack back and forth – Measure the motion of robot wheels, as part of dead-reckoning robot positioning systems. By accumulating the result of a robot’s wheels driving it along a surface, an estimate of overall translational movement can be made. A pair of encoders is used on a single shaft. The encoders are aligned so that their two data streams are one quarter cycle (90 deg.) out of phase. When rapidly sampling the data from the two encoders, only one of the encoders will change state at a time. Which encoder changes determines the direction that the shaft is rotating. Copyright Prentice Hall, 2001 12
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9-9 Decision to Sell Products at Split Off or Process Them Further     Joint Joint product product costs costs incurred incurred prior prior to to the the split-off split-off point point are are sunk sunk costs costs — — not not affected affected by by aa decision decision to to process process further further after after the the split-off split-off point. point. AAproduct product should should be be processed processed beyond beyond the the split-off split-off point point only only ifif ifif the the incremental incremental revenue revenue exceeds exceeds the the incremental incremental processing processing costs. costs. Value is added only if the incremental value from processing exceeds the incremental processing costs.
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Steps in Incremental Analysis 6 Step 1: Compare revenues under both alternatives Step 2: Compare costs under both alternatives  Additional costs decrease profit.  Cost savings increase profit. Step 3: List and clearly label each incremental revenue, incremental cost, incremental cost savings, and opportunity cost.  Include a + sign if the incremental amount increases profit  Show the amount in ( ) parentheses if the amount causes profit to decline Step 4: Total the incremental amounts and label the effect on profit. Costs that do not differ between the two decisions are not relevant, so omit all irrelevant costs, including sunk costs.
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Pricing Special Orders (3 of 4) Learning Objective A1: Use variable costing in pricing special orders. Exhibit 19.19 Should the company accept a special order for 1,000 pairs of skates at an offer price of $22 per pair? Reject Special Order Accept Special Order Incremental sales $0 Incremental costs 0 Incremental Income $0 Incremental sales (1,000 × $22) $ 22,000 Incremental costs Variable production cost (1,000 × $15) 5,000 Variable selling expense (1,000 × $15) 2,000 Incremental Income © McGraw-Hill Education. $ 5,000 19-65
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7 Keep or Drop Example Data reproduced: Units sold Revenue Variable costs Direct fixed costs Allocated fixed costs Operating income Snacks 800 $49,600 19,200 10,000 16,000 $4,400 Salads 1,200 $52,800 26,400 14,000 18,000 ($5,600) cont. Sandwiches 2,400 $67,200 33,600 13,000 16,000 $4,600 Total 4,400 $169,600 79,200 37,000 50,000 $3,400 Incremental decline in salad revenue ($52,800) Incremental variable cost savings - salads 26,400 Incremental direct fixed costs savings –salads 14,000 Incremental snack revenue (10% x $49,600) 4,960 Incremental variable costs –snacks (10% x $19,200) (1,920) Incremental decrease in profit if drop salads ($9,360) Original profit +/- Change in profit = New profit New profit = $3,400 - $9,360 = $5,960 loss
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4 How to Make Process Further Decisions If incremental revenues < incremental costs Sell as-is, unless qualitative characteristics impact the decision If incremental revenues > incremental costs Process further, unless qualitative characteristics impact the decision If incremental revenues = incremental costs Use qualitative characteristics to assess
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4 How to Make Outsourcing Decisions If incremental cost savings < incremental costs Continue to make internally, unless qualitative characteristics impact the decision If incremental cost savings > incremental costs Ousource, unless qualitative characteristics impact the decision If incremental cost savings = incremental costs Use qualitative characteristics to assess
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Additional Relational Operations (cont.)  OUTER UNION Operations    The outer union operation was developed to take the union of tuples from two relations if the relations are not type compatible. This operation will take the union of tuples in two relations R(X, Y) and S(X, Z) that are partially compatible, meaning that only some of their attributes, say X, are type compatible. The attributes that are type compatible are represented only once in the result, and those attributes that are not type compatible from either relation are also kept in the result relation T(X, Y, Z). Copyright © 2007 Ramez Elmasri and Shamkant B. Navathe Slide 6- 61
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Summary ° Decoder allows for generation of a single binary output from an input binary code • For an n-input binary decoder there are 2n outputs ° Decoders are widely used in storage devices (e.g. memories) • We will discuss these in a few weeks ° Encoders all for data compression ° Priority encoders rank inputs and encode the highest priority input ° Next time: storage elements! ENGIN112 L17: Encoders and Decoders October 10, 2003
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