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Product of Sums reduction using Karnaugh Map - dyclassroom
There are a couple of rules that we use to reduce POS using K-map. First we will cover the rules step by step then we will solve problem. So lets start... See more
Consider the following 4 variables K-map. Now we mark the cells in pair (set of 2) having value 0. 1st pair = (W+X’+Y+Z) . (W’+X’+Y+Z) 2nd pair = (W+X+Y’+Z’) . (W+X’+Y’+Z’) (the … See more
Consider the following 4 variables K-map. Mark the cells in quad (set of 4) having value 0. 1st quad = (W+X+Y+Z) . (W+X’+Y+Z) . (W’+X’+Y+Z) . (W’+X+Y+Z) 2nd quad = … See more
In this we consider that the K-map top edge is connected with the bottom edge and left edge is connected with the right edge then we mark the pairs, quads and octets. Lets check few examples. See more
Consider the following 4 variables K-map. Mark the cells in octet (set of 8) having value 0. octet = (W+X+Y+Z) . (W+X+Y+Z’) . (W+X+Y’+Z’) . (W+X+Y’+Z) . (W+X’+Y+Z) . (W+X’+Y+Z’) . (W+X’+Y’+Z’) . (W+X’+Y’+Z) (the octet is in Product of Sums POS form) … See more
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Introduction of K-Map (Karnaugh Map) - GeeksforGeeks
Online Karnaugh map solver with circuit for up to 6 variables
Online Karnaugh Map solver that makes a kmap, shows you how to group the terms, shows the simplified Boolean equation, and draws the circuit for up to 6 variables. A Quine-McCluskey …
A Karnaugh map provides a systematic method for simplifying Boolean expressions and, if properly used, will produce the simplest SOP or POS expression possible, known as the …
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Karnaugh Map Solver | Free Online K-Map Simplification Tool
Free Karnaugh Map Solver: Simplify Boolean expressions from Truth Tables, Boolean, Minterm/Maxterm inputs. Generate SOP/POS with step-by-step solutions.
Karnaugh Map(K- Map): Definition, Working, Methods …
Learn about Karnaugh Map (K-Map), its working, steps to solve expressions in SOP and POS forms, advantages, disadvantages, and applications in logic simplification.
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Karnaugh Map : Working, Rules & Example Problems
Sep 24, 2021 · The karnaugh map method is very fast and more efficient to convert the truth table of Boolean expression into simplified SOP and POS form. All the rows of the K-map are represented by square cells, which are …
Plotting Karnaugh Map with examples - Electrically4U
Feb 14, 2024 · Plotting a Karnaugh Map. A logic function either in a truth table format, SOP expression, or POS expression format can be easily plotted in karnaugh maps. Each K-map is the extended version of truth tables, in which …
We can minimize Boolean expressions of 2, 3, or 4 variables very easily using the K - map without using any Boolean algebra theorems. The K -map can take two fo rms Sum of Product (SOP) …
K-Map (Karnaugh Map) - Sanfoundry
The Karnaugh map (K-map) is a visual tool for simplifying Boolean functions, organizing truth table values in a grid based on Gray code. Looping in K-maps involves combining adjacent cells (for SOP) with 1s or (for POS) with 0s to …
KARNAUGH MAP SOLVER FOR FUNCTIONS (POS) - MAD for …
Online K-map solver with product of sums output for 2, 3, 4 and 5 variable functions. POS Karnaugh map solver for boolean functions.
Karnaugh Map solved examples (three, four and five variables K …
Nov 2, 2022 · In this tutorial, there are several solved examples of mapping the standard and non-standard POS and SOP expressions to the K-Map. I tried to make this as simple as possible. …
K-Map Generator SOP POS Implicants - GitHub Pages
Online Karnaugh map generator, which can take up to 4 bits of variables, and solve up to 8 distinct sets of outputs at a time. For each output, a color-coded corresponding K-Map is …
Karnaugh Map Solver - AllMath
To use the Karnaugh map calculator, select the type of calculation i.e SoP or PoS, name the output (optional), enter the “ Input names ”, and click calculate button. What is a karnaugh …
• Karnaugh map (K-map) can be used to minimize functions of up to 6 variables. –K-map is directly applied to two-level networks composed of AND and OR gates. •Sum-of-products, …
Product of Sum k map | 3, 4 or 5 variable karnaugh map ...
The steps to map a standard POS expression. STEP 1: Determine the binary value of each sum term in the expression. These binary values make them equal to 0. STEP 2: Map 0 on the …
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![Example: Solve a Product of Sum (POS) expression using KMAP [3 & 4 variable]](data:image/jpeg;base64,/9j/4AAQSkZJRgABAQAAAQABAAD/2wCEABsbGxscGx4hIR4qLSgtKj04MzM4PV1CR0JHQl2NWGdYWGdYjX2Xe3N7l33gsJycsOD/2c7Z//////////////8BGxsbGxwbHiEhHiotKC0qPTgzMzg9XUJHQkdCXY1YZ1hYZ1iNfZd7c3uXfeCwnJyw4P/Zztn////////////////CABEIAOEBkAMBIgACEQEDEQH/xAAbAAACAwEBAQAAAAAAAAAAAAAAAQIFBgQDB//aAAgBAQAAAAD3cm5OTk5MbGMYwYMAABgAAKmq+uPLdzreC/qDQ1lXpvKgLC6OOgNDPO+d33ZnWmd7uqguqu2o9PQ2JQF/30+d96/T9boaq/oOjZ4wvunI6XMfQTL8dnYUXTaY/aYn6Os9w9/Ha0Ghx1v53uYv/bg09PnedaTwrunm5uvx0+QtufQ47ss9GV1NX2XHdXHz7Z4z6QuXDdek86DQ5qHPr8jss5z72nztiqvWToZ0l9V2HJ30OqzO9GUNIr73zErHQYX26NxiuT6BUUGhoNVh9XxUnrLcVDcnIk2xtttjHEmJTBiYAABFtVDk6vgJW9QdlvQeV3Ot02Uv6G39qi1qdNm+Ht02YuCmuc6dV7mloa7quAVQ5Pyra7R8VRcddUWtLbUGizGtykL+svaG8oNlj72i0JndHl7/ALK2quO2u7boFUOTdbVauoqLbvpOu6qPfO29JrsrYVPfe0NzUbXF2tLflDocve2E6Xg973p7AVQ5N11Xqami9Ou4zRadlTrsVp8xrqHwu6LXY7yNrVZ00fvk/TpvcyXnj23YKocm23JtNsclMYMGclBo+gAYgBgCqHJtc/t7tptkODy8eB6Txz6v+7LwuplwNAwBgCqHJ1lTGVldyG35+mU0+a6eSwpdJ7ZLU5m66rXG7QJjABgCp5PjoD27X0W6ciPri9rlObs0eL1Htj9jU8/BvcHvUwAESAFTt1VU7myjU3pJseavaPuuiqzxf9mXhbX2W2AwAQSAFTN1NdZHbz+9ipOQ+fjtiQSUoesSr6ewJACCQAqZ+VQWcn7enopSkNkfSKmpkZkGxekgEA2IKVUfP2d3T5e/vIlJuQkekZyjIYMAYACkAKl56KPR3+/pL39SU22RJQ9JQ9SHq4tg4kgBNgRpa2tl3da9OSz9ycpNkgSkOcJoUPXy9I+0ZCBsCNFTefV3+0yv9e+c5SByh6xYpTh6CbAAYgbELKcfTAtOllP0WM5x9GSAByIzJDABiENgjGesIepYdhn/AEvPSYxekZSITAAk4zbAEDYhYj1IS6vDv9uTwt+mUm22yIMABwYwGRF4KXv64+PR5ePv7+Vj4eNt6zk2B5JJoaioJRSilFRiQIFpTx8jt5Pd9suG295yk2LjQE4gpeQKIhCU4HmwcObh6vN+nb1VVp1Tk5DOcUXJRIuCSiQIogiMvM7PR1nJDoDs9eHv7PWUm2BBACioiiklGMVFJ+8u3yWfPHo9vKwl4dfX7+jlJgwAAABgITDzmw//xAAYAQEBAQEBAAAAAAAAAAAAAAAAAQIDBP/aAAoCAhADEAAAAM0CgAAQAAAFszbKACWwAAAAzShCglKQAACAlLCgAAAAAIJQsoAAAAACCUAoAAKSWkAgJTUlAKEFQBUAgJSsdLNYAACiKQCAlrHSas3yAAACwAgJdTn1mt87kAAACwCArU5dcb68rmUAAApAIWOuKrl0l3jFBFuBQKAEM66ZoXj13zxQ1jnE3iXWNyam6zuxrUs1PJ6u/HWa4dtZyQpjXDWCa3jO9K1F0XOs78vo6Y1kxupABKIoAAiv/8QAMBAAAgICAgAFAwQCAgIDAAAAAQIDBAARBRIQEyExNBQgMhUiMDNAQUJRIzUkQ1D/2gAIAQEAAQgA+4f/AJZ/FvC1fnhnkjSlPJYjZ3u3vpiI44b92eQIgBAG8v3ZqrxLH+r28rSGeGJ8sctOk8qRVuVtTTxRtnJX3qGJIv1q5kbrLGki25ngqzSp+uXc/XLuUeWE7iKfwu3oqSKWk5u852kfN3VP76d2K5H2S1bhpxh5ZecuP+Cc1fHvQ5SO2fLe1K0NaaVP129h9z4XeVu1bMsOcXee4knmXbH0tWWYR8zfldI15KzLUqiWOly1uxahhfkbMtSqZY4+es9181JElRXS/wAraq3JYU421LbrGWS9yMNLQMnOXn9o+bvL70eRhugjD+LeF/5k2VrYrVH0A0jgZVqrWj148z/dBnQ+WHzi7HSlOcVCyyHKHzIMA2QMvT/U2ppMtVjWMOcNP3rmI8l8CzkIDSxg36lCOpMwUsGBXw50P9WhNC1DVlLSztxN8oco8elRjInMTGW9IucPRhnDzS2+MrSwP0VijBltSebxcsngfc+HPQbEM44WbpdCZz82kggzg4O9oy5znwBnFf8AsKuc38A+HF8iar+XJzH/ALGc5wXwstzmzZmmPFcdAayzTXuOqTxbgqcbZr2YZcP4t4X/AJk2RxvK4RHRonZGo2fPh9eUllRYPKgntGeEHmf7oMhQyUbWJM0ccsYSPXGTyZR+ZBl6byKcz5H08xO/J3KtuOPy+Ln8m2mcl8CzgBYgD9OvZQ4mUSrLY8Lz8a+4LQ4lZwXqWak9UgS8JO62DDnKIUv2c4Jwa0qZNIsUE0jZKpTh2U4QdnNHLkH1NWaLI5GikR15KyLVyWVeHg8mkhznPgDOL+fWzm/gHKECWLUcL2qslSYxSEk+/BfDx0ZHZG45hLxihJ+Lt14Wlkp/LrY34t4X/mTZxQHkyHOUg2onFac15VcIysoZNnOZ/ugzh0EiWULAqxU2YxDw0SZR+XBnNT7kigFGgbnfP0P/AKBIOxZmE/ESS5B/dFn+z9nL0JZmE8UFq1TZhFPas23Uy8RQkhJnl5TjjaAliDWKsuxNbs2ABLQ4uWV1kn5D4Nrw+onypPMbdYHOUgEF2YCvCZ544gFCgKOd+AM4r59XOb+BnEfPgy7Tjuw9GlikhkeOTg/hHOW42QytYgisT1yTEZbt5lQxwSV+Qgikb8W/yGRX9GVET8fAqGGmWONPVf8ABaON/wAgAo0uN+LfbfuWK8qLF+qXs/VL2DlL2cjZmrRQmL9Xv5+r38o37c9lI5LFiKrEZJJeYuOf2Lyt9TlHkktHo/J2ZqtZHhpcndntQxuo2y5Py19J5UHGzSWK0cks/LX0mlQcbyAtr0k5KeWtUMkVDk7s9uGOTlLE1WqJIaPKXZ7cMcjMqKzvZ52Ukit+r8lvK3OzAgWUdZFV0u8pehtzxpxdiazV7zcnPLWqeZFT5W9NbgjflLE1aoJIv1nkc/WeRylyl6a1DG927HSiDvJzV9/ZOZ5FfehyKXVIzlL92rbKR8RbtWhOZ/Fvxb7ZK8ExDSclWghro0dFEktRI/0NPOZ/pgym8CTqZ/quHyqaU23g5mQmyiZxNaOZ5Hku0opoH6QUb8U0bjm/hx5SmSC1FK45ylkziSaVxw3woctfJnyOR4nV0t3UucUTnFfPgznPgrnGfPr5zsvSrFHlCBbNuKJvpKmuucjWWrbkiTgZS1eWPOS+fazhPgHOZ+BnHfPqZzfwBlVoksRNN9ZweU342dya/Pqe9d8pWhUnEpnu8XfCCajQqwsJ6/PofOrvnBJqm5+xvxb7uX+LHnHfNh8OZ/pgypXNqYRD9BkylSamkgPLqRcJzhH/ALo8mlEEMkrJzRdlUc38OLK0P1E8cWDhN61KnlyOmcP8KLLPyZ8nof8AwoLUW84v58Gc58Fc4z59fOeTcNZ84qRIr0Jf1zlpEkvS9OATUc75yXz7W+EcfRuM5pgtJUbjQTfq5zfwBlaH6ieKHP0A5Q400TKcu2aC7gtrxlW33NO1x9mmA0nDzPHdRRytGW4sHShXNaqkTeLfi33cqCa0YHHo4uQ7zmATDBirMh2ve3lB7Btw979P6uMaeOes+2eaxYID0eOm/vk5n4cOcarpegYxDTRZZjc2JyOJBFKHdhHNiYilsUq+cpxpgfzYOMRxegJ5oE0Uzjo3F2Dc8CWIXhezx9qsT2Fy15fl5VrPbmESV4ErQpEnK8a87efArWKr7BM9qTZ4rjXgbz5uaBNEYEmUgjvcym9o2oO3LUHthJIg1qm+xJYtWyqycTx0sUonm55Wa1DrggRXn+xvxb+EfefUEYMG8DITobzeb8N+G9azsOxXxu047kRRk4a+jB0ieQIBZ/wW/FvuZ0jXs5vVBkViCU6T79gZsEDOStGrWSNeGhVIXnbk71yC46R/qnIYvLX1OVLgt1jIL/JCm/VJOTvyHZXkr6kHKHJC2/R7dkVIDM83LX5T6G7yURG+N5VrDiCfm6wkqibOHumeIwPhIGt4fY4vb/kvtr+Nvxb7BlnkepKQPK8h2+DK9949LIrBgGX7TJtNgA6HXlJTLemyvE0UMSZy41efOIeqgmM3JvWe0TX4BdtPu1KZ7E0p4mtGleGXOVrRS1JZMhkaGVJF51CakZFed60yTI/L1rUXlWqVfinfzoPK82KRX46Uw3YGzT+ZvHUthTsoDdV1rAOg0oAAAH8Tfi32XpvKg6g+EcbOdBKsoyeqUHYcdOfWE/YRsEYQn/INphlwFbdgHfqM5j575WpzWu3lpw1s+9WvHUhVEnjMU0qHiJVlqwoOWlWGk+4o2lkSNbN2CBU89K3F35Sle5xE1SIzZWkeKxE6InRtCM9raEH3P+A34t9nJ+8XgoJOhVgZB2YZKhdCBWQx3EU4PsKhvfqu+2czD0teZlKUTVoXzlYJ5LjsvDxSok4k0xIxO3Rc5DjDa/8ANE1a3A3qILczDOO4swETT36a2oRGHo3YH9SLsvo3HcVKJUmntTeRVnlzh4DLcRv8E/i32XtuygIndwuLGI/ZGeR+i1mZjkrM8yx5BGPMifwH2E6zY/blyqLcYjPFwW4C8UpO0GOTtDgYemJ+CZFvooO/XWN2JTW9Dbb7Mh8O/vnZSdDlYrdlEhgo1FpwBPH2P8x/FvGWQRqWIlEkrjI0CSDFAYYK6ZEwDYUjds6/uXxHiVBzXthOimHXvh2GBzbYQT1OI+lUYGOftUnWzmzgAQoAW0DgOlOI/YsMDvpjinF7bbZ32YhvbX8x/FvAnQJyeYyvvAerAgT+ay5Gc7gDO0QbeI6HQUHxHjv2zfqBh1+wns/uZE2ynGUKjFQqD22VixHDKCDv9px369BgII2D+cfgNga+7X8x/FvCy/WF/GuNs2IxX0PYMNYsf/Urxwhdqd+A+zW9HNDYOOQACey61hfbbxmiYaJPsFVlK6Jb0Ol33JPbCfRtK2zH2zRw7J0PYfaJIz7dh17fePtb8W8Lz+y4cSJ5DkcXT0zoGGeUc0VUkk95EJj/ABHiPH/rNgEDGOlJwtoqMYnS4xb2Us+v2xlygOL3I2T22mOzKpI9cYHceaOFFPuvuwyQ6AOKWWJgq792XSb76fzN4GcufBPQEfcPtb8WxzoE5O3d/QJrXYOiKOiASxq4UZrGXY1k9f0MirYEa+qsGUMBg8SN6zr+7eP/AFvjBiV0W/f0wg+hBJjUtkf44kagjQcMY9SBmQqo3677q3TXhoHR+89v9ABQAPtH2t+LZNJv30CTvrB5ZxYw0ewsjprrBJHONYB/3rAoJIwbjJGQTP2TsMHhtw6LgZe2sUlvXNq6nNYV2MIOf6BzQXQzZGs6ja5pvbNNnQLo4TobwbA232b9dfxD7T+LYqmR9tEnV/SQKH9N6I11UvJoh4upyvaMuo3De2/QKcEroHATtuIMMGDNfuDZrZJwdupGdG6uoYHS6Ct0UBwCV7N6o2ezNuUOSNEMWVsUEE7Xsoc5ENFQqkdUOSgsFGEyFF0zEdRjMR10+gxw+hX+Ifa34tgJwSSa6qYpNFy3sNqwBGyjSKdodMNxqAG6aH7tPB2k3GXft3MDeZEjYB/DsYWGd1zuud1zsuFkI0e6Z3TPMTPMjzvHjPCffzos8+HPPhwzQ4JoT7edDnmx/wC/Nhzz4M8+DDZrjHvxqf2/qMefXwem0swS/gfVW1HEpK4yiNth2DKj4EEoQZrf7sedmXRjiQIiPG3SdDkYPsX/AGxoMZQs3XEAUAAYPu9MMijOwPrgIPt2XCQBs9lGs7rhIHvmwfbCRmx92jmicIIzRPsQR7sCPcqw1tgR6Exya3gBY6V0dR+6pPH5RhUTJtiXdpW9CCMUAn1Qyt/41I0xGQnu3ltYYO/bEYSRp2lTujJgYOw3ExZRsYPuOsUAyOCn/wBgwf1tmh0Bz08rAoKLuNQRsv6vrEP7CMT2Ph/s4fbxOE4SRjEgDB+Bx/RNGQlVGn9UQlwG2pk/OHD8gYZJBMwEbdWl7OCYWKU1mjYuDCjDWGBkH7JUAiTezkbgoqYo7ls/FsDAum4wwRhnsw3GGM37YfRFwYPvaAEk55YUEYEABGeUudB11gGhrFXqPQRr650A3roM9gMKjNeJzeE7wkkZ2OiMLHrrBIR6Yzs2ts7MQcaVmKktIxYPn1D4kroTp53ZeuU/qTGMHhfk/CPGX9nbATrWRL2jcmchpOyw781SE9EmLFkDMwKvEVfIt4p9MH3+maBzy88s55bZ5Zzy2zy2zynzypM8qTPKkzyJM8iXes8ibPp5s+mmz6afDVnw1p8+msYa0+fTWM+msZ9LZw1bOCjabBxkmhscZ/3HGybDDDlr5jZN/wAfA/EyfIf7VwfjNj/nJk/4x5F7Ynti+I/mb2OD2/iP2Ni+3i/4Nn//xAA4EAABAwIDBAcIAgICAwAAAAABAAIRAzESIUEQUVJxICIyU2GSsQQwQEJygZGhE8FD0VCjM2Ki/9oACAEBAAk/AP8AkeE7MEBRIdCg1PmnRCn5UZO/ZhgskyEKflV3BBmBryBIWCHO3bIxkS6UKXlVnNBCjE0CJQpeRCl5E0MebEbRie6zEWM5MWB6ycO01a9louUGU09jubAm4KqjExkhCl5NopqMbCoxCA2d5QpS4x2FE4wFgh71E4wExhYnS1wkFYIbCicZCGOobMRYzk1Fj+bEMFQXYuE7TNUv6qzc4/srNx7R290rEwv8MlfK2f3C49lphvIL56TXq9Mrc1WLwmMY+7IKuDltsaQhUBUBCrGg76FXLw9qOVOGBNxQYAVJrHhpLSEYIMgr56Ads37PoKtUBavF5VqQXfNXGu9bsM0XL/0XelfM5MD3PX8LKqrUMniz1wnaJJQhzTBR67MnKo4TinCVWqkGo2ZcV3SuxzHq1QAH7GV81ZjVxq5GBvNynBIxRuWPG0qz+odgkkwF7O9CA0yG7asOC9qZUbOoLUyJsUZY8LjlXD12WsOy49mbsBQKuWy3mFdrgQuxZivUONd81ca71qs6V9jvCMrvShBaSCr4HsQYGhd6xcJ2jPGriA9Ws4bwjLSMoRK7pWcAFcGFfGwrjCPYEu5lPwBq9ok/Rs1Y1cbeiJyh4VRzN4VRzzohBiGhf+VqL6Tx9iqz3gWBKZFMLg2Vn+Yqq+DVZrss442q73AIQAAByC74LjXet2ZOGbHJsOaYIXelNkO7bVUewm8FOq1joFGJtVi4T8Q0HmJTGt5CNoBHimNHIAfBMa7mAUABuGzhPReACybAqqPI1VR5GqqPI1OAJcZyBVVvkYqrfIxPBb9AC5NaLuKLaY3AKtPMAoBlVOhxqQqgLSeALeFVEB5HYajLi4qsIDyOw1QKwTodjaqoLPoCdDjVAVWWE8ATg1rRJJTQxu8iSvaSmh7d4EFEFrgCCqsNa8gDAE6XYyE6HYwFVlrqgBGBqdDv5AFXHkYq48jFVlpdwBCXO7DVVDBuaFXxIYKjbhVIZgaRkE+YiOhwno0w4gQqYBNRCWlUGrjchLIOkqj/ANapAYdcMKzKYTQQxUmioM2YRCoHqvBXfoEtaZMJlZWc8lcZXeOTi1zTIKyeKjMY2d+1cS/yPXZN17PSj6V2btXyPXeld89aVgu+au+ahNMOlwVD/qVABzNcEK2AhUhUQq0nBVy9a0lrV6HCfTpd7t43IxIKqnyIl0ndC1Y3ZZo/JXsrPMV36cG4jEle1M8pRnC4hcRXeOQ+QGoNvftXEtHuCMAyEEZAgKxeAhB/lK0qlHrvqyu8BXfNRjG6JVf/AOE/HjRuJiF7UYbcPagCwmA4I5VMnIsBZNyiC4Ekx0OE+nS7xNOzjcg8HeJCdV/JTqkKBUZZNexwsVUfU3AmU2IEsaV3qaRBWjR6pjoNRyByemOg1HK+AJk0nJhXfNTXASrOCpkt42qvUwbsSIVghL4h7EX0n+Uovqv8xQh9mtXfBMeCNQCnVvyU6rH8jVm9iNSk5VH1NwTY4AgTFBd50OE+nwGoWmx7CdwcCenqYRzG0Q8dhyfTBCNJtQXh1/guE9JwaPFVCeTVUBO6x9ycUOBdAlGKtUfhqBlyrPYAxi9qqL2glCHjIhAPqkBe0vXtNQ/UZQArLPOA3eVWLBuYq9ccyVGM2er0kZfT2EZ7CRyup5EyjMEj8GPd8J9OjH1pxJ2y5qMgiQek0G8i9k7kDmrMOAKzWARMhcDFUptMiJUFuESRYlDgV3PJTZe9xQAewSHK7XArSogC5hkSvZnxvY5F80uur1WEHwkLV0FHLCoiIIzCMmLoCEIPvOE+nQu8xtCbs5t6OoI/KEg52mIQMYonxXeuUAYVwMWHLeYRpgKTmC46lXa8hdumXSEYe8YWhXe4AJjoeXiA1GtTenhzArhwTiQDABMwtao9fgeE+nQ3HYJKGwIb+lKAnerVRKZJDYJVF8YGKmW5jtBFuU6HVHQaBOH8qpVGlUqjiVGPRqhrplpVF/NqFZ/gZKEBpkNWjDHMq1Prn4HhPp0IhrZOzKBdYpic3IlTBMSTkEIgP6QK1Rgw4tO4phDZyIfYrUhTfQK5sFwhNIgBaHNCYM5lZQJK3u2ERp4oglUpZd5kLN5zefgeE+m0r5h0MgbKCtJ6U/YwtFNyMuSbUkiDGX9oOze2G5aKn+0GiDN06nYfMi1EDE8E9Upw8pRP2b/tB0Q7KAmuTcmsJvNguYzH9Jli6M9ye5x8ZAUXyQdPynQLX33CfTachZaFMjCI2iUI6euzR39FBuH9gJzpxtETkmSYTR9giB1LkwAYRnILenAS5GQuF/q34bhPps3R0jCOZsOnpsIADmzKqsw8xKqMw4xAlFpG4p2UtsfHNFHOMsimnN9zeIQKmUetDhYj12Bfc9J7fysx4e84T0Mh0DkAnAkn3BEnRaQf2tZXG1RJEyU2XTBzhYW30J1WWZERuKdqdPBGTyTv0E49o6DcU535Qlb0YzvEx4o44BAdaUB9l25MmDmjlg/tCoOsb2jZZriB7vhKOy6IkHMaIRPQyIujj/1vVj0d4KOoMeIELcPVOiDNgVBgsMo5hDEZl2i3n1U/dxN14n1RAJ3iUQj8w/Y91l4+84SuYCKcCbgxmhmCZMowjD1fZYo3JaVMPkfcdC0OM705s7pVkZCc7zFF3mKNQ8iUXx9RTn8g4ou86JnRPP4CcPwg0AZmBo0IT/acPQfCcJQPWMgBMkgu1kiEb3AWYkIF0ZgBGJzBCHW0cFB0kFHMzZS6d+akOD55DoaNITjaI0WTohOvhj7LMh0okQdQJidUCWxunNXI/ZWpyUxhiBH9pxEaJonM4t8okmXEIOgCDIiSuyCYPhoUXAZ4oiYIhAB0iU4tBBlwQmSmA9TG42XiPf8ACdhgE2GSEAbLajeEMGETnkiQNSLjkog9dsJ8zm0LLE0OCPg5aj3ZGwoohEQUU4JwTwntRTlUH4KqBVWqo1VWeYJ7BzcFVp+YKqzzBVmflVqawO+7v9IN8xP9Koz7ByqA8yAVwlOBk2C6zdCbFPvM6wU4dUQV2ZgICy7TxOV06WzE7wVMY4v1fut7mqQ0mDKsOmEE4IjY4IohOCIGw+5BQQhAoIEJpzsgQUwoElNIVOtYzD5ahJJkDQFN+w2GG2KYOyL5wFvREPKAgjRHtth31NW6RzC3G+8q9jzHuChqVbCVvTZ3lcSHyoZyjkB7wwjMoq8hXW8rgQm8NTC2TMjMBVMTfHNMqddhHVAIhAIA6EbwmFsCDz2DW/gsgBJRmCoDQsyHMd5kLPi8zvKElsn3Rv4rXZKmJlbtmfNTmifdxtuEBksig2d6gzeVAHgmn+ITFwNvMq2KEUOpHWM7kIBAKbiIzARzlqMy4la2I94UQoUIhQoTU1NQH5QTP2Ez9hNH5CaPyEz9hU1SP5CpFUXKi5UXKl+XNTG+cKsAfpT2/tVGuwsNsf8AZO3e1cR2byuF3qFuK75q3f2u8/4fhK//xAAmEQEAAgECBgIDAQEAAAAAAAABAhEAAyEQEhMxQFEgQQQUMlAi/9oACAECAQE/APJPJPhf+gY/6V+OYuOHjVjwPFOC8A8UMoycK7cIblZVeJXGcDuZDJfKnKcpyn1lOU+sp9ZT6yn1lPrKfTnJJ+s6c/TiJ3PgmGzk/r4GR1my4lKhnXkhsfzbhrSk/wDIfzedaZpk0LXbI63M6Z9SM1tV0yNF25DVkzjFDeN4a8nUlGthyGrqTqiO5Zn7Gp0+dI/1WR/InIiES5KDn7actx93WH5TQsT+Fzr6hBWMVoSnI6nW01ascJJg2cZd8m7HxjHTG+Uzk0ULDA0ztXas5dLYo27Z09F+jJR05ANIZ09BrY2w09EbovIx0YtgDhHSqtqu86eilVHveENErY2wholbRzl/HiJRvknSjHlgHA4vfJfXif/EACkRAAICAAUCBgIDAAAAAAAAAAECABEDBBIhURNAEBQgIjFSMkFCcIH/2gAIAQMBAT8A/pkDuALgh7YRZUbYduoqXCb7ayIr34OK7hGvaPB6bAnUT7Ca0+wmteRNa/YTUvImpfsJrXkTUvImociWOZqXkTWvM1rzLB9ANEGUN9/mD0MKEfLijTmwAT/s8ogLWSfdpEOXRACxP5lZ5ZDjdMFqUW0fLaFxTvasAJl8FcUvqNUI+CoRmUnZqhyyDDU3uwj4OEhNlvaaO08thdTQGb8bjZZFLksaVQSJ5QHXTcVDlRZAb+YEGBhlgAzAWQbEbD6TgC6IhUGEUfEAGjFG59FTE6ritZl5pS1E7w+Yb5s73LzNsfdbfMGJmh+2itjoSVsEzqZkXu2815grpJNRmx3ADEkTVjWTvdVBiY4N211UL4xuy28L4xuyfm5rx2IOo7QdRmtyfA/PjxF7T//Z)
