Digital System Fundamentals: Don't Cares in Logic Simplification
Explore the concept of Don't Cares in digital systems, how they help simplify logic, and their application in 7-segment decoders. Learn how to use Don't Cares efficiently in K-maps to optimize circuit design and minimize complexity.
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ECE 352 Digital System Fundamentals Don t-Cares Don t-Cares 1 1
Dont-Cares Don t-care Conditions For some circuits, we may know that some input combinations will never occur Sometimes it doesn t matter what the output is for certain input combinations that can occur In either case, we don t care what the output is for some input combinations Can use this info to help simplify logic We can choose outputs to be either 1 or 0 for those input combinations, since it doesn t matter We can choose values for these outputs in a way to help us minimize the K-map more efficiently Don t-Cares 2 2
Using Dont-Cares in K-Maps X represents don t-care locations K-map groupings can include X s X s do not have to be covered with groupings Notes: The don t-care X is not an output value The actual output will be a 1 or a 0 based on grouping 1 if in a group 0 if not in a group Do not add more implicants just to cover X s Makes hardware bigger and more complex than necessary We do not need to force those minterms to be 1 we can choose to make them be 0! Don t-Cares 3 3
Dont-Cares: 7-Segment Decoder Many displays are LEDs arranged in segments Ovens, alarm clocks, DVD players, speedometers, etc. Lighting different segments forms different shapes A common type is a 7-segment display Often used for displaying numbers 0-9 Need a logic function to control each segment based on a four-bit BCD value 7 segments 7 logic functions If the input is a BCD digit, perhaps we don t care what is displayed for values 0xA through 0xF Don t-Cares 4 4
Dont-Cares: 7-Segment Decoder Assume 1 is on, 0 is off unless told otherwise! Active high it is active when the input is 1 Active low it is active when the input is 0 Example: ACTIVE LOW Find SoP equation E(D3,D2,D1,D0) for bottom-left segment E E = 0 for 0, 2, 6, 8 E = 1 for other valid BCD values Don t care what E is for invalid BCD values 0xA 0xF 0000 0001 0010 0011 0100 Don t-Cares 0101 0110 0111 1000 1001 5 5
Dont-Cares: 7-Segment Decoder Can go straight to the K-map since it is a truth table D1D0 00 01 11 10 D3D2 00 0 1 1 0 Don t-Cares Enter 0 in K-map for D = 0000, 0010, and 0110, 1000 Enter 1 for all other valid BCD values Enter X (don t-care) for all invalid BCD values 01 1 1 1 0 11 X X X X 10 0 1 X X E = D0+ D2D1 6 6
Dont-Cares: 7-Segment Decoder An X is not a value in digital logic We only use it as a placeholder here! D1D0 00 01 11 10 D3D2 00 0 1 1 0 Don t-Cares 01 1 1 1 0 Don t-cares that are in a group become 1s in the function Don t-cares that not in any group become 0s in the function X 1 X 1 X 1 X 0 11 X 1 X 0 10 0 1 E = D0+ D2D1 7 7
ECE 352 Digital System Fundamentals Don t-Cares Don t-Cares 8 8
