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> <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~~