DontCares ECE 352 Digital System Fundamentals DontCares 1

Don’t-Cares ECE 352 Digital System Fundamentals Don’t-Cares 1

Don’t-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 2

Using Don’t-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 Don’t-Cares • 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! 3

Don’t-Cares: 7 -Segment Decoder • Many displays are LEDs arranged in “segments” Don’t-Cares – 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 0 x. A through 0 x. F 4

Don’t-Cares: 7 -Segment Decoder • Assume 1 is on, 0 is off—unless told otherwise! Don’t-Cares – “Active high” – it is “active” when the input is 1 – “Active low” – it is “active” when the input is 0 5 • Example: 0000 0001 – ACTIVE LOW – Find So. P equation E(D 3, D 2, D 1, D 0) for bottom-left segment E – E = 0 for 0, 2, 6, 8 – E = 1 for other valid BCD values 0101 0110 – Don’t care what E is for invalid BCD values 0 x. A – 0 x. F 0010 0011 0100 0111 1000 1001

Don’t-Cares: 7 -Segment Decoder Don’t-Cares D 1 D 0 00 D 3 D 2 11 10 00 0 1 1 0 01 1 0 11 X X 10 0 1 X X E = D 0 6 01 • Can go straight to the K-map since it is a truth table… • 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

Don’t-Cares: 7 -Segment Decoder Don’t-Cares D 1 D 0 00 D 3 D 2 11 10 00 0 1 1 0 01 1 0 11 X 1 X 0 10 0 1 X 0 E = D 0 7 01 • An “X” is not a value in digital logic – We only use it as a placeholder here! • Don’t-cares that are in a group become 1 s in the function • Don’t-cares that not in any group become 0 s in the function

Don’t-Cares ECE 352 Digital System Fundamentals Don’t-Cares 8