Build a combinatorial digital logic circuit using components in your lab kit to
ID: 3877510 • Letter: B
Question
Build a combinatorial digital logic circuit using components in your lab kit to implement the following Boolean function. The circuit should take in three one-bit inputs called A, B, and C, in the form of three voltage divider circuits built from a 10,000 ohm resistor and a push button switch. These three inputs should be built as active-high, that is, pushing a switch button should create a high voltage to send to the combinatorial logic portion of the circuit. NOTE: Keep in mind that the inputs you built in lab were active low (1 when not pressed/ 0 when pressed).' The combinatorial circuit to be built treats the input bits A, B, and C as representing an unsigned decimal integer from zero (inputs ABC = 000) to seven (inputs ABC = 111) me of the decimal numberi represent an element of fzero, four, fivej, then the circuit output is to be a logic 1 represented by a high voltage. When the number of letters is odd, e.g., {one, two, three, uld be a logic 0 and a low voltage.Explanation / Answer
The Karnaugh delineate (or K-outline) a strategy for improving Boolean variable based math articulations. Maurice Karnaugh presented it in 1953[1] as a refinement of Edward Veitch's 1952 Veitch chart,[2][3] which really was a rediscovery of Allan Marquand's 1881 consistent diagram[4] otherwise known as Marquand diagram[3] however with an emphasis now set on its utility for exchanging circuits.[3] Veitch outlines are accordingly otherwise called Marquand– Veitch diagrams,[3] and Karnaugh maps as Karnaugh– Veitch maps (KV maps).
The Karnaugh outline the requirement for broad estimations by exploiting people's example acknowledgment capability.[1] It likewise allows the quick distinguishing proof and disposal of potential race conditions.
The required Boolean outcomes are exchanged from a reality table onto a two-dimensional matrix where, in Karnaugh maps, the cells are requested in Gray code,[5][3] and every cell position speaks to one blend of information conditions, while every cell esteem speaks to the relating yield esteem. Ideal gatherings of 1s or 0s are recognized, which speak to the terms of an authoritative type of the rationale in the first truth table.[6] These terms can be utilized to compose a negligible Boolean articulation speaking to the required rationale.
Karnaugh maps are utilized to rearrange genuine rationale necessities with the goal that they can be executed utilizing a base number of physical rationale doors. An entirety of-items articulation can simply be executed utilizing AND entryways nourishing into an OR door, and a result of-aggregates articulation prompts OR doors bolstering an AND gate.[7] Karnaugh maps can likewise be utilized to improve rationale articulations in programming plan. Boolean conditions, as utilized for instance in restrictive explanations, can get exceptionally confused, which makes the code hard to peruse and to keep up. Once limited, authoritative entirety of-items and result of-totals articulations can be executed straightforwardly utilizing AND or potentially rationale administrators.....
K-maps for Sum-of-Product Design
•A negligible aggregate of-item configuration can be made as takes after:
• Create the K-delineate, a 1 or 0 in each square as indicated by the coveted rationale work
•Beginning with huge rectangles and going to little rectangles, include rectangles until all minterms are 'secured' (all '1's are incorporated).
• Generate the arithmetical terms comparing to the rectangles
....
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