Cmn=Am2/Pn=M!/(n!(m-n)!)=Cm(m-n)
由于是键盘操作,故取n=2,m>=2
m=2时. C22=2!/2!/0!=1 即最小组合键需要2个IO.即2线1键
设2个IO为Pin0,Pin1.
组合扫描为Key1=Pin0,Pin1
m=3时. C32=3!/2!/1!=3 即3线3键.
设3个IO为Pin0,Pin1,Pin2.
组合扫描为Key1=Pin0,Pin1
Key2=Pin0,Pin2
Key3=Pin1,Pin2
m=4时. C42=4!/2!/2!=4*3/2=6 即4线6键.
设4个IO为Pin0,Pin1,Pin2,Pin3.
组合扫描为Key1=Pin0,Pin1
Key2=Pin0,Pin2
Key3=Pin0,Pin3
Key4=Pin1,Pin2
Key5=Pin1,Pin3
Key6=Pin2,Pin3
m=5时. C52=5!/2!/3!=5*4*3/6=10 即5线10键.
设5个IO为Pin0,Pin1,Pin2,Pin3,Pin4.
组合扫描为Key1=Pin0,Pin1
Key2=Pin0,Pin2
Key3=Pin0,Pin3
Key4=Pin0,Pin4
Key5=Pin1,Pin2
Key6=Pin1,Pin3
Key7=Pin1,Pin4
Key8=Pin2,Pin3
Key9=Pin2,Pin4
Key10=Pin3,Pin4
m=6时. C62=6!/2!/4!=6*5*4!/2/4!=15 即6线15键.
设6个IO为Pin0,Pin1,Pin2,Pin3,Pin4,Pin5.
组合扫描为Key1=Pin0,Pin1
Key2=Pin0,Pin2
Key3=Pin0,Pin3
Key4=Pin0,Pin4
Key5=Pin0,Pin5
Key6=Pin1,Pin2
Key7=Pin1,Pin3
Key8=Pin1,Pin4
Key9=Pin1,Pin5
Key10=Pin2,Pin3
Key11=Pin2,Pin4
Key12=Pin2,Pin5
Key13=Pin3,Pin4
Key14=Pin3,Pin5
Key15=Pin4,Pin5
m=7时. C72=7!/2!/5!=7*6*5!/2/5!=21 即7线21键.
设7个IO为Pin0,Pin1,Pin2,Pin3,Pin4,Pin5,Pin6.
组合扫描为Key1=Pin0,Pin1
Key2=Pin0,Pin2
Key3=Pin0,Pin3
Key4=Pin0,Pin4
Key5=Pin0,Pin5
Key6=Pin0,Pin6
Key7=Pin1,Pin2
Key8=Pin1,Pin3
Key9=Pin1,Pin4
Key10=Pin1,Pin5
Key11=Pin1,Pin6
Key12=Pin2,Pin3
Key13=Pin2,Pin4
Key14=Pin2,Pin5
Key15=Pin2,Pin6
Key16=Pin3,Pin4
Key17=Pin3,Pin5
Key18=Pin3,Pin6
Key19=Pin4,Pin5
Key20=Pin4,Pin6
Key21=Pin5,Pin6
m=8时. C82=8!/2!/6!=8*7*6!/2/6!=28 即8线28键.
设8个IO为Pin0,Pin1,Pin2,Pin3,Pin4,Pin5,Pin6,Pin7.
组合扫描为Key1=Pin0,Pin1
Key2=Pin0,Pin2
Key3=Pin0,Pin3
Key4=Pin0,Pin4
Key5=Pin0,Pin5
Key6=Pin0,Pin6
Key7=Pin0,Pin7
Key8=Pin1,Pin2
Key9=Pin1,Pin3
Key10=Pin1,Pin4
Key11=Pin1,Pin5
Key12=Pin1,Pin6
Key13=Pin1,Pin7
Key14=Pin2,Pin3
Key15=Pin2,Pin4
Key16=Pin2,Pin5
Key17=Pin2,Pin6
Key18=Pin2,Pin7
Key19=Pin3,Pin4
Key20=Pin3,Pin5
Key21=Pin3,Pin6
Key22=Pin3,Pin7
Key23=Pin4,Pin5
Key24=Pin4,Pin6
Key25=Pin4,Pin7
Key26=Pin5,Pin6
Key27=Pin5,Pin7
Key28=Pin6,Pin7
如果加"独占键"即8个IO的接地键,那么8个IO不加如何器件的键盘个数为28+8=36个.
"组合键"的程序很好编写,可能比行扫描更好编~~~不要被它吓到,问问数学家~~~
祥见菜农的"键盘论"~~~
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