#Floyd digital fundamentals 10th edition pro
The circuit can be drawn directly, as shown in Figure 8-2 In this experiment, you will use the Karnaugh mapping method, similar to the one described pro viously, to design a BCD invalid code detector AS you know, BCD a 4-bit binary code that repre- sents the decimal numbers through 9. The resulting expression is the sum of all of the product terms. Since each group in this case is a group of four l's, each product term contains two variables (two were eliminated from each term). I's will eliminate three variables Figure 8-1 shows the groupings for the 2-bit com- parator. A group of four l's will eliminate two variables and a group of eight. A group of two adjacent I's will have a single adjacent boundary and will eliminate one variable.
Within cach group larger than one, adjacent boundaries will be crossed, causing the variable that changes to be eliminated from the output expres. 0 11 11 0 0 0! 1 1 11 11 10 1 11 11 1 one of the product terms in the reduced output func- tion. For simple combi- national circuit, truth tables are used to summarize all possible inputs and outputs the truth table com pletely describes the desired operation of the circuit The circuit may be realized by simplifying the ex pression for the output function as read from the truth table A powerful mapping technique for simplifying combinational logle circuits was developed by M Kamaugh and was described in super he publishedħ. c.) and should contain only The largest possible group should be taken all I must be in last one group and may be taken in more than one group if bepul Aber grouping the l's on the map, the output function can be determined Each powiada Summary of Theory With combinational logic circuits, the outputs are determined solely by the inputs. The size of the groups must be an integer power of 2 1. The map can be read in sum-of-products (SOP) form by grouping adjacent cells containing 1 on the map. The corresponding values for the output function are entered from the truth table. In this example, the map is drawn using numbers to represent the inputs. All possible inputs are clearly identified by the truth table and the desired output for every possible input is given Next the Karnaugh map is drawn, as shown in Figure 8-1. The inputs will be called AA, and B2B The desired output is HIGH if A,A, is equal to or greater than 8,8 To begin, the desired output is written in the form of a truth table, as given in Table 8-1. The output variables appear as O's and I's on the map in positions corresponding to those given in the truth table As an example, consider the design of a 2 bit comparator.
(Adjacent cells share a common border hori zontally or vertically.) When you are drawing a Karnaugh map, the variables are written in a Gray code sequence along the sides and tops of the map Each cell on the map corresponds to one row of the truth table. The method involved writing the truth table into a geometric map in which adjacent cells (squares) differ from each other in only one vari- able. Build and test a circuit that implements the sim- plified expression Predict the effect of "faults" in the circuit Materials Needed 7400 NAND gate LED Resistors: one 330 m, four 10K One 4-position DIP switch in 1953. Tenth Edition CHAPTER 4: BOOLEAN ALGEBRA AND LOGIC SIMPLIFICATION Experiment 8 Logic Circuit Simplification to Objectives After completing this experiment, you will be able Develop the truth table for a BCD invalid code detector Use a Karnaugh map to simplify the expression. Transcribed image text: Floyd, Digital Fundamentals.
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