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introduction_to_digital_systems:realization_of_comb._logic [2023/03/27 11:31] – mexleadminintroduction_to_digital_systems:realization_of_comb._logic [2023/09/19 23:48] (current) – mexleadmin
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-====== 4. Realization of Combinatorial Logic ======+====== 4 Realization of Combinatorial Logic ======
  
 ===== 4.1 Preparation ===== ===== 4.1 Preparation =====
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-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. +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, the inverted inputs are usually drawn parallel to the inputs. 
  
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 ==== 4.1.1 History of the Logic Families ==== ==== 4.1.1 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 that define the internal logic.+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 that define the internal logic.
  
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 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. 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 logic is based on CMOS. <imgref pic04> shows that this type of logic only dissipates a fraction of the energy loss (and therefore heat) compared to the older logic families. This started the logic circuit development, which lead to mobile phones, computers, and all the other present digital controllers.+Modern controller logic is based on CMOS. <imgref pic04> shows that this type of logic only dissipates a fraction of the energy loss (and therefore heat) compared to the older logic families. This started the logic circuit development, which led to mobile phones, computers, and all the other present digital controllers.
  
 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. for adjusting the logic voltage level.  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. for adjusting the logic voltage level. 
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 ==== 4.1.2 Logic Stages==== ==== 4.1.2 Logic Stages====
  
-From the <img pic02> we know what the logic for the sum-of-products looks like. in <imgref pic05> also the gate logic for the product-of-sums is shown. +From the <imgref pic02> we know what 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: Both consist of two logic stages:
   * For sum-of-products the first logic stage is set up with  OR-gates, the second stage is the AND-gate,   * For sum-of-products the first logic stage is set up with  OR-gates, the second stage is the AND-gate,
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-When there are programmable connections, the IC is called programmable logic device (PLD). Depending on the position of the programmable connections, these PLDs are separated into (see <imgref pic07>):+When there are programmable connections, the IC is called a programmable logic device (PLD). Depending on the position of the programmable connections, these PLDs are separated into (see <imgref pic07>):
   - Programmable Array Logic (PAL):   the first stage is programmable, the second stage is fixed   - Programmable Array Logic (PAL):   the first stage is programmable, the second stage is fixed
   - Programmable Logic Element (PLE): the first stage is fixed, the second stage is programmable   - Programmable Logic Element (PLE): the first stage is fixed, the second stage is programmable
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-In <imgref pic10> the simulation shows a PLE. in the top left corner the address is shown in decimal. The logic enables only the address ''0'' up to ''8'' to have an output. The address increases and therefore step by step the information - given by the right-side array - is read. In the bottom right corner, the memory of the address is shown in decimal. By clicking on the switches on the right side, the second stage one can also reprogram the stored information.+In <imgref pic10> the simulation shows a PLE. In the top left corner, the address is shown in decimal. The logic enables only the address ''0'' up to ''8'' to have an output. The address increases and therefore step by step the information - given by the right-side array - is read. In the bottom right corner, the memory of the address is shown in decimal. By clicking on the switches on the right side, in the second stage, one can also reprogram the stored information.
  
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 PLA was often used as glue logic but is nowadays rarely in use. <imgref pic11> shows the principal setup. PLA was often used as glue logic but is nowadays rarely in use. <imgref pic11> shows the principal setup.
-Based on PLAs - and in special on PLEs - more complex logic devices are developed.+Based on PLAs - and especially on PLEs - more complex logic devices are developed.
  
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   * There are also **Field-Programmable Gate Arrays** (FPGA). These have a huge number (>100'000) of simple functional blocks. One functional block contains the logic gate circuit and storage elements. Between the blocks are broad binary busses. The logic circuits, storage elements, and bus allocation can be changed by reconfiguration. In <imgref pic12> the logic gate circuit is represented by a truth table. The storage element called flipflop will be investigated in the next chapter.    * There are also **Field-Programmable Gate Arrays** (FPGA). These have a huge number (>100'000) of simple functional blocks. One functional block contains the logic gate circuit and storage elements. Between the blocks are broad binary busses. The logic circuits, storage elements, and bus allocation can be changed by reconfiguration. In <imgref pic12> the logic gate circuit is represented by a truth table. The storage element called flipflop will be investigated in the next chapter. 
  
-FPGAs can be used to test new microcontrollers and microchips. For this, the FPGA is configurated in such a way, that it resembles the new chip. +FPGAs can be used to test new microcontrollers and microchips. For this, the FPGA is configured in such a way, that it resembles the new chip. 
    
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