Don't Care Terms

Objectives

1. Understand why don't care terms exist
2. Understand how to deal with don't care terms in K-Maps

Notes

• Carpineli has some information.
• Wikipedia is a good supplement
• The Seven Segment display is a common component.
  • 7 or 8 inputs
  • a-g drive the lines
  • The last one drives the .
  • (wikipedia)
• So there are seven inputs,
  • Labeled a-g
  • 
  • For the one in Digital, a-d are across the top from left to right.
  • e-g are across the bottom left to right
  • . is on the bottom far right.
  • 
• If we wish to display 0-9
  • To display the digits 0 - 9, we need 4 bits.
  • Some of the patterns (A₁₆-F₁₆) we don't care about.
  • We designate don't cares with an X
  • Carpineli gives us this table of logic to light the proper segment when a 4 bit number is input.

  • b3	b2	b1	b0	a	b	c	d	e	f	g
    0	0	0	0	1	1	1	1	1	1	0
    0	0	0	1	0	1	1	0	0	0	0
    0	0	1	0	1	1	0	1	1	0	1
    0	0	1	1	1	1	1	1	0	0	1
    0	1	0	0	0	1	1	0	0	1	1
    0	1	0	1	1	0	1	1	0	1	1
    0	1	1	0	1	0	1	1	1	1	1
    0	1	1	1	1	1	1	0	0	0	0
    1	0	0	0	1	1	1	1	1	1	1
    1	0	0	1	1	1	1	1	0	1	1
    1	0	1	0	X	X	X	X	X	X	X
    1	0	1	1	X	X	X	X	X	X	X
    1	1	0	0	X	X	X	X	X	X	X
    1	1	0	1	X	X	X	X	X	X	X
    1	1	1	0	X	X	X	X	X	X	X
    1	1	1	1	X	X	X	X	X	X	X

  • So if we wanted to build a table for the "a" segment

    • ab\cd	00	01	11	10
      00	1	0	1	1
      01	0	1	1	1
      11	X	X	X	X
      10	1	1	X	X

    • When we go to circle in a 4x4 table
      • Two rows or two columns represent a single term (8 cells total)
      • For terms (one row, one column or a square) represent a two input and
      • Two terms represent a 3 input and
      • An isolated cell represents a 4 input and.
      • Don't cares (x) can be a 0 or a 1, we don't care

      • ab\cd	00	01	11	10
        00	1	0	1	1
        01	0	1	1	1
        11	X	X	X	X
        10	1	1	X	X

      • In this case, all the don't cares were used, but they didn't have to be.
      • c
      • a
      • abd
      • a·b·d
    • So the function for the a segment is a + c + abd + a·b·d a·b·d
    • 
• As a side trip, they make BCD to 7-segment decoders/drivers
  • We will use the word decoder for something else later.
  • The 7448 is such a decoder.
    • 4 data inputs, A,B,C,D, A is bit 0, D is bit 3
    • 7 data outputs a,b,c,d,e,f,g
    • voltage and ground
    • lt
    • bi/rbo
    • bri
    • The not lines are normal.
      • These are "active" when the value is false.
      • lt is the lamp test
        • When the lt is low, and BI/RBO goes from low to high, all segments are turned on.
      • bi is not blank input.
        • If this is low, no segment is lit, regardless of the input.
      • bi/rbo acts as a clock, look at the timing diagram on the datasheet.
  • 
• The digital file