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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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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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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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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Overvie w ° Binary decoders • Converts an n-bit code to a single active output • Can be developed using AND/OR gates • Can be used to implement logic circuits. ° Binary encoders • Converts one of 2n inputs to an n-bit output • Useful for compressing data • Can be developed using AND/OR gates ° Both encoders and decoders are extensively used in digital systems ENGIN112 L17: Encoders and Decoders October 10, 2003
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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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Quadrature Shaft Encoding Which direction is shaft moving? • Suppose the encoders were previously at the position highlighted by the dark band; i.e., Encoder A as 1 and Encoder B as 0. The next time the encoders are checked: – If they moved to the position AB=00, the position count is incremented – If they moved to the position AB=11, the position count is decremented State transition table: • Previous state and current state are the same, then there has been no change in position • Any single-bit change corresponds to incrementing/decrementing the count • If there is a double-bit change, this corresponds to the encoders being misaligned, or having moved too fast in between successive checks—an illegal transition Copyright Prentice Hall, 2001 13
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Incremental Analysis Components Incremental Revenue The additional revenue as a result of selecting one alternative over another Incremental Cost The additional cost as a result of selecting one alternative over another Incremental Savings The reduction of cost as a result of selecting one alternative over another Usually combined with incremental costs 3
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Operating Cash Flows – Indirect Method FiCo is deciding whether to purchase equipment with a cost of $74,000, an estimated residual value of $6,000, and an estimated life of 8 years. FinTru predicts the equipment will reduce annual payroll costs to $360,000 from the current level of $423,000. Cash operating expenses related to the new equipment are expected to be $41,200 per year. FiCo’s cost of capital is 7.4%, its required rate of return is 8.8%, and its income tax rate is 31%. Calculate annual incremental operating cash flows. Incremental payroll cost savings ($423,000 - $360,000) $63,000 Incremental cash operating expenses (41,200) Incremental depreciation ($74,000 - $6,000)/8 (8,500) Income before taxes 13,300 Income taxes expense (31% x $13,300) (4,123) Incremental net income 9,177 Add depreciation 8,500 Operating cash flows $17,677 9
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Operating Cash Flows – Shield Method 10 FiCo is deciding whether to purchase equipment with a cost of $74,000, an estimated residual value of $6,000, and an estimated life of 8 years. FinTru predicts the equipment will reduce annual payroll costs to $360,000 from the current level of $423,000. Cash operating expenses related to the new equipment are expected to be $41,200 per year. FiCo’s cost of capital is 7.4%, its required rate of return is 8.8%, and its income tax rate is 31%. Calculate annual incremental operating cash flows. Incremental payroll cost savings $63,000 Incremental cash operating expenses (41,200) Incremental depreciation (8,500) Income before taxes 13,300 Income taxes expense (4,123) Incremental net income 9,177 Add depreciation 8,500 Operating cash flows $17,677 Depreciation tax shield = $8,500 x 31% = $2,635 $63,000 (41,200) -21,800 (6,758) 15,042 Cash basis income 2,635 $17,677 Tax savings: $6,758 - $4,123 = $2,635
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Incremental Approach Solution Incremental cost to buy (1,000 x $23) Incremental cost savings: ($23,000) Direct materials 9,000 Direct labor 5,000 Variable overhead 2,000 Supervisor’s salary 4,500 Incremental decrease in profit if outsourced ($2,500) Should DP outsource? Based solely on quantitative analysis, no. Outsourcing will cause profit to drop by $2,500. Only relevant costs are listed on the incremental analysis. 7
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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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Incremental Encoders • Encoders typically run on +5V, not +24V • Outputs are typ. not 24V compatible either
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Incremental Analysis Components Incremental Revenue The additional revenue as a result of selecting one decision over another Incremental Costs The additional costs as a result of selecting one alternative over another Incremental Savings The reduction of costs as a result of selecting one alternative over another Often combined/netted together Opportunity Costs The amount given up as a result of selecting one alternative over another 3
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Preparing a Single Column Incremental Analysis 5 Step 1: Compare revenues under both alternatives • ‘Change’ in revenues = relevant revenues Step 2: Compare costs under both alternatives • ‘Change’ in costs = relevant costs and cost savings Step 3: List and clearly label each incremental line item • Display as a positive amount if the incremental amount increases profit (i.e., a benefit) • Display as a (negative) amount in ( ) parentheses if the amount causes profit to decline Step 4: Label the bottom line as ‘Incremental increase(or decrease) in profit if ………………..’ (replacing …. with the nature of the analysis)
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Keep or Drop Products or Segments  Relates to whether a company should drop a product or segment that appears to have an operating loss, or keep it • Incremental cost savings and incremental revenues are relevant – Incremental costs will result if demand changes occur in other products/segments  Caution  Allocated fixed costs are not usually eliminated and must be absorbed by other products Cost Allocation Death Spiral A single column incremental analysis is prepared.
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Special Orders  Two types  One-time-only orders  Goal is to recover all incremental and opportunity costs  Long-run orders  Goal is to recover the full cost of products and opportunity costs  Companies cannot operate successfully in the longrun without recovering ‘all’ costs  Incremental revenues, incremental costs, and opportunity costs are relevant  Capacity considerations are relevant A single column incremental analysis is prepared.
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Process Further Example A company manufactures two models of door locks using the same production process. The costs incurred up to the split-off point are allocated $100,000 to each model. Additional data follows: Product X Z Number of Selling Price at Selling Price after Additional Units Produced Split-of Processing Processing Costs 5,000 $10.00 $15.00 $14,000 4,000 19.40 21.60 12,000 Prepare an incremental analysis for product X. Incremental revenue (5,000 x ($15 - $10)) $25,000 Incremental costs (14,000) Incremental increase in profit if processed further $11,000 Process further because profit is expected to increase by $11,000. 5
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ple: Calculation of Incremental CF Incremental cash flow = cash flowB – cash flowA where larger initial investment is Either of the costAlternative alternatives B shown below can be us a grinding process. Tabulate the incremental cash flo A st cost, $ nnual cost, $/year Salvage value, $ B B-A -40,000 - 60,000 -20,000 -25,000 -19,000 +6000 8,000 10,000 +2000 The incremental CF is shown in the (B-A) column R on the extra $20,000 investment in B determines which altern ct (as discussed later) 8-4
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Incremental cash flows Incremental cash flows are the increased cash flows due to investment  Do not get confused about the average cost or total cost?  Do you have examples about incremental costs?  Incremental Cash Flow = cash flow with project - cash flow without project Financial management: lecture 6
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Stacked Auto-Encoders • Stack many (sparse) auto-encoders in succession and train them using greedy layer-wise training 10
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9-4 Encoders 9-4 Encoders • Most decoders accept an input code & produce a HIGH (or LOW) at one and only one output line. – A decoder identifies, recognizes, or detects a particular code. Digital Systems: Principles and Applications, 11/e Ronald J. Tocci, Neal S. Widmer, Gregory L. Moss Copyright © 2011, 2007, 2004, 2001, 1998 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 • All rights reserved
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9-4 Encoders 9-4 Encoders • The opposite of decoding process is encoding. – Performed by a logic circuit called an encoder. An encoder has a number of input lines, only one of which is activated at a given time. Shown is an encoder with M inputs and N outputs. Inputs are active-HIGH, which means that they are normally LOW. It produces an N-bit output code, depending on which input is activated. Digital Systems: Principles and Applications, 11/e Ronald J. Tocci, Neal S. Widmer, Gregory L. Moss Copyright © 2011, 2007, 2004, 2001, 1998 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 • All rights reserved
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TurtleBot Mapping Using Kinect Sensor Bar The TurtleBot uses information from the Kinect IR sensor bar and internal Gyro and encoders to build a map of its environment. Using the GUI loaded in linux you must start the mapping program and then teleoperate the robot via an adhoc network and drive it around the area. The robot will then create the map based on its position given by the gyro and encoders, as well as any objects/walls given by the kinect sensor. Navigation and Mapping Sources/Videos http://www.ros.org/wiki/Robots/TurtleBot (Video and Info) http://profmason.com/?s=TurtleBot (Images/Video and Info) http://www.youtube.com/watch?v=VIQChgUacJI&feature=player_embedded http://www.youtube.com/watch?v=fljcaI4MDfA&feature=player_embedded Map GUI 9
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Wireless backpack Will work on existing Finches Will work with existing software Android too! Adds ports for distance sensors, prototyping, and encoders • Anticipated Cost: $99 for backpack, $35 for rangefinders, $35 for encoders. • Live Demo • • • •
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ENGIN 112 Intro to Electrical and Computer Engineering Lecture 17 Encoders and Decoders ENGIN112 L17: Encoders and Decoders October 10, 2003
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Autonomous Mobile Robots, Chapter 4 4.1.3 Wheel / Motor Encoders (1)     measure position or speed of the wheels or steering wheel movements can be integrated to get an estimate of the robots position -> odometry optical encoders are proprioceptive sensors  thus the position estimation in relation to a fixed reference frame is only valuable for short movements. typical resolutions: 2000 increments per revolution.  for high resolution: interpolation © R. Siegwart, I. Nourbakhsh
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Turbo Codes  The information U can also be encoded using 2 encoders:  Motivation: using 2 simple encoders in parallel can produce a very effective overall encoding  Interleaver causes permutation of inputs
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Encoders • Opposite of decoders – Encode given information into a more compact form • Binary encoders – 2n inputs into n-bit code – Exactly one of the input signals should have a value of 1, and outputs present the binary number that identifies which input is equal to 1 • Use: reduce the number of bits (transmitting and storing information) w0 2n inputs w2n – 1 03/24/19 y0 yn – 1 UAH-CPE/EE 422/522 AM n outputs 42
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Encoders: Priority Encoders • Each input has a priority level associated with it • The encoder outputs indicate the active input that has the highest priority (a) Truth table for a 4-to-2 priority encoder w3 w2 w1 w0 0 0 0 0 1 03/24/19 0 0 0 1 x 0 0 1 x x 0 1 x x x y1 y0 z d 0 0 1 1 d 0 1 0 1 0 1 1 1 1 UAH-CPE/EE 422/522 AM 44
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Encoders • Opposite of decoders – Encode given information into a more compact form • Binary encoders – 2n inputs into n-bit code – Exactly one of the input signals should have a value of 1, and outputs present the binary number that identifies which input is equal to 1 • Use: reduce the number of bits (transmitting and storing information) w0 2n inputs w2n – 1 03/24/19 y0 yn – 1 UAH-CPE/EE 422/522 AM n outputs 8
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Encoders: Priority Encoders • Each input has a priority level associated with it • The encoder outputs indicate the active input that has the highest priority (a) Truth table for a 4-to-2 priority encoder w3 w2 w1 w0 0 0 0 0 1 03/24/19 0 0 0 1 x 0 0 1 x x 0 1 x x x y1 y0 z d 0 0 1 1 d 0 1 0 1 0 1 1 1 1 UAH-CPE/EE 422/522 AM 10
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Shaft Encoding Reflective Optosensors as Shaft Encoders • It’s possible to build shaft encoders by using a reflective optosensor to detect black and white markings on an encoder wheel • Wheels can be used with any of the reflective optosensor devices, as long as the beam of light they generate is small enough to fit within the black and white pieshaped markings Copyright Prentice Hall, 2001 40
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Wheel Encoders • Two types of wheel encoders reflectance sensor slot • Note that there are two transitions sensor per rotation (dark to light and light to dark)
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