DW EditSeite anzeigenÄltere VersionenLinks hierherAlles aus-/einklappenNach oben Diese Seite ist nicht editierbar. Sie können den Quelltext sehen, jedoch nicht verändern. Kontaktieren Sie den Administrator, wenn Sie glauben, dass hier ein Fehler vorliegt. CKG Editor ====== Realization of Combinatorical Logic ====== In the last chapter we investigated the Therm-o-Safety example. From this, it was possible to create the logic formula via sum of products of products of sums (see <imgref pic01>). <WRAP center> <imgcaption pic01| gate logic from Therm-o-Safety example: Formula> </imgcaption> {{drawio>Thermosafetyformula}} </WRAP> It is simple to derive the gate logic from the formula (<imgref pic02>). For each of the three (min)terms an AND-gate combines the needed inputs. As shown in the image, usually parallel to the inputs also the inverted inputs are drawn. <WRAP center> <imgcaption pic02| gate logic from Therm-o-Safety example: Gate Logic> </imgcaption> {{drawio>Thermosafetygates}} </WRAP> The main question is now: which generalization of the shown logic can be found? ===== History of the Logic Families ===== A huge variety of integrated circuits (ICs) were used historically. <imgref pic03> shows two separate integrated circuits: There can be single or multiple gates in an IC with two or more inputs. The most used IC series was the 74xx ICs, where the xx are numbers which define the internal logic. <WRAP center> <imgcaption pic03| integrated circuit> </imgcaption> {{drawio>integratedcircuit}} </WRAP> The logic families which were first developed were based on bipolar transistors. To use these as an closed switch a constant current is needed. This result in relatively high power losses. Depending on the combination of these transistors this logic families were called "transistor transistor logic" (TTL) or "emitter coupled logic" (ECL). The name TTL survived as a designation for the needed voltage levels $0V$ and $5V$. The $5V$ can still be found as supply voltage in some logic circuits. Modern controller an logic is based on CMOS. <imgref pic04> shows that this type of logic only disipates a fraction of the energy loss (and therefore heat) compared to the older logic families. This started the logic circuit develompent, which lead to mobile phones, computer and all the other present digital controller. The 74xx series is nowadays mostly from historical interest. Nearly all of the applications can now be done directly with microcontrollers. In rare cases they are still used as "glue logic" between two logic ICs, e.g. as for adjusting the logic voltage level. <WRAP center> <imgcaption pic04| (historical) Logic Families> </imgcaption> {{drawio>Logicfamilies}} </WRAP> ===== Logic Stages===== From the <img pic02> we know how the logic for the sum of products looks like. in <imgref pic05> also the gate logic for the product of sums is shown. Both consist of two logic stages: * For sum of products the first logic stage are the OR-gates, the second stage is the AND-gate, * For product of sums, it is just the other way around: first logic stage AND-gates, second stage OR-gate. Generally, the two-stage setup allows to implement any possible logic based on a truth table. <WRAP center> <imgcaption pic05| Logic Stages> </imgcaption> {{drawio>Logicstages}} </WRAP> Often a simplification of the circuit represenation is used. There the multiple input ant output lines are reduced to one single line, representing a bus (= multiple parallel lines) . This can be seen in <imgref pic06>. <WRAP center> <imgcaption pic06| simplified representation of the stages> </imgcaption> {{drawio>Logicstagessimplified}} </WRAP> <WRAP><well> <imgcaption pic0x|Simulation of an Inverter></imgcaption> \\ {{url>https://www.falstad.com/circuit/circuitjs.html?hideSidebar=true&ctz=CQAgzCAMB0l3BWEBGGAmOaDsWyQBxoBsAnCViApJSACwQICmAtMsgFDJWVEoYj5qyfshrUEnBGhAZxRfDLggiS0RHHsAkgJS8FtaoehIJAGR0KFzBdOoAzAIYAbAM6Mx7AO4hmaWhZ1ILwCFZF4g70E+alloqGDYhClFIX4IlLjY-AV02OQSaUT5eO8imKVif3TmLGkrWt0Sn1R-err48xr2rp8bFBBHV3ckIO0esJ8GgygoY0otHzQwaQnfZbpDWZN2TqXuvd6ZGcG3D29fIlbFy4Ec4Iurtfbqg6sDiZf16afbjpRhARCAE3FYDZynEb3MKhSD+aYtJqsZLfLh1O7nVE6JErcJQ-CPTHo5r4rHIEnZP7Y0nJaxHUQnYbxMaY1aY6ZGbbnCkI2gwqrsADKi15KFhwssOWO4Pc1DAguaxQRrGKFJiYKGMzl5z8lmovhFqqhKr10N+1QpUWsEviQqtov8dtV-QZmqhYqsCMN5ymeoaXsOlutQVtfIDkvp0td2sefjNwX01CDwQQvCVofSKf+0hFbFswRzAJzYvS8LF8LS+dScjiGdTaAU62ERMb9fAK2LwUbYv16fYGAoPcBwuoN38HH7Ct1CpHcJQfcgA4teqio7nE9pURndDXC8OmKEYF4Y-ni9CNKiyEP2-Hu+VZ+kyoPR53A51KBpfif187KywvEHyB-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-6M9LUtzt4XyWm+vKCesVD+MbgmZpbbaUB2iNSyQvCwy7TQy1EMvuyWQ1DQ5NtHhSTX+sjy4B00DZwfoOOA2AcF0bQGNfWbhxJ1UU3-ddtI62nsc9PHD5TPnCKFzddDJ-tqd2unMx-TK2fB2rwcl8Uucq-nptq6blcq5apq15sV1yrapsm01JXWcttk117Q2Cb1VsJ85FcEc0yRl1Sg8NRHnsLwcm8HNv2o3Ifo6x177v43QPuSNWtDu5fqZiOl3CwzRUuxrlMz5UOtDA1MWMpUrb8AqmXaqbY9QHzQltDYCY4EqQ3qAzE4C8QgJNCSVBCkEFNQICNQcBgqZR1sJdGyek254PUuAqeWcZ5vjACSQcWDWYMPZsQxEFJWH7VQSdQh3DEKkOnm6dB5dmEF1AQ0MRDZGHsODGnShsjM4NzoSIuizCGz8FkThBBOc8EQVoBMJqHx0J0EMQmIkMs8EyyAajf+-h35r1husL4e0XGkwQRTHRps9GC3oYwxmh4BbrlNFw9WgSxa3k4TI2UbdlbSIzuE2WkTwAAhiO7JJPMwAAmsGk58WsqHZOUmgdJyt6HZMZsUvJP5wBXiYVeTxh5ZQE3qdoxp9s2lITAMkTMXS8xOxqUeWUyRfbgGlg5AZTQeljJFGAMZEEwC1IbC08irxIGaQ+nHCsX0FkkTWUPMhXIUkPg0QvBoBxxEL3uusVgYpljiW4Ysk5It1S0IGkc7hFZYFZIfCEz5o1vn-K2Sw2pvyZIvOUWZGZtT6FpBoRC7BOzxmIq6v4c5K87mILqj8pBlziiIumMi+4BxzkHz+RVElp8-lRF6TISRwy77wRpdStqL8JAuCzO+Pi+4lHBFzJyjlm5aZ8ovPwVcHBcYoCvDmZZ4zLxB35SMwkXERnCyOjYxGNgrHbUmXjLVTMmh8uFny-c7B2WGpotq-ZQxTUcsqb8O1Vq3C8oBHa81ji8ZzxkIKjVXqpY2Fvj6u1R1b5moBFwqJGd67OoJm5F1AbGVtwbMUEZiT4kezTRG+IobsyZibuEHl3g+W5z5Vw-RnsNaCSauW3OIzc55qzRyqQ1om113BdGygrYi2S20QgQsChe19PGQOodrYRktopC23ISgUz8x4IJUWM79UpiJElHgoQ4JJEHauzdGQd25BuDu6+e6EgHuKFjelpQoiLvrHIIkR6OZXrCvemIUx43XzsbS6Qy6mhHuSNfGlQQOoNG-dfFQQhwA-wSHSwofo71KDAxkIgxjSgNAQ6B4xABZRDExYhEBAjIYw7AsPobxqh-DaBCMAA9rhCEoUsUIbBtxRGgOwajvVaMegQAx0QrRqAsbY2QUU9QKBsB40OfjzQSBCYg6JpjfHWPEhQF7JTEBeMgAk8wEgGFfS4VU+JhTrAsBSbJCaBAIn8B6eYwZmGxmTZgHM5Z+TbGbMyA-PZ1zSA1MacAlJmG2KKAw08-pgTNgaRAUC3J9TBmySuezB5yLGniCym+PR0ZjmotsZM6M0zDZ6AJYM4J2ZvoKCzPS95qTRWIOlfy85pDpiHxLCkwYoLVnMv4B44UhATWuA1aElLbJWB9A9a89Z-rhRTEtac4sLrDkGbud5BQEbmWjOzfXot-Ai3gs+C06tmoQdNutcU7yWcC3etkmM8DRjwgDtTfOwhPGV3BNLaU75s9jHsBicO0lh2MRCAOzKwp77-8bB-foJ9qb32ukeoJjNkbJ84Q3AqggGVPxa4-GRwjde2ZEeYgxypTCOOSR46cmWHHYpif3GLg6YDKPYxo9jBT8itd+0tOCe6Zo2TmYAA18krw9AnbnaBfGPGudzoI64spvAaDnEAXO5QTmYkh1MxQ8NxYAJpazfErsaI4vggDV+kRXOH4PIe+trkj8RnPdKIA1gxPAgvTES908euULPbkd9Z5I2v9SiCQ01jYGXptfp2z75QkAxMe+W+IQTSIpMqDi5H5oWARyAXXnH-gcIpuGfEO1tPlBMIB+88nngEBY88GfInmoPA4spgd1nigXGDZcb05Xig2v-B+-d-XygO2O-h674H6wUmuv1AUCoCPWf8Bx9WIN5Q+QB8aan-n30-a3eZ8H0vlMRd+1EDr4H5YX6sBWwWZQHAC+FPVbM1bBA9iz-r4k1wq-4ASAmDv4Xi-eHT9WyP6fzbieun6CxiHhNbYDn7Ub2YgFLyfx-5TYLKAFWwPx0CgH34X6p4frLCAEwH75JAHRqBEB4x07v7gHhZoBqAba8woHgFdK4GjIEEnawHICoqkFthIDCyUHKDB5Sa4Bh4J5TY25z4UDcE24GyJ78FcaiDcFcb0GB5iGf6SH4Hn4ABGiwE6BBygeA8QyhXAHeqm06MM8QQAA noborder}} </well></WRAP> ~~PAGEBREAK~~ ~~CLEARFIX~~