Author: Gerd Isenberg
Date: 15:10:02 06/01/04
Go up one level in this thread
On June 01, 2004 at 17:45:50, Gerd Isenberg wrote: > >Btw. one needs only four odd/maj pairs to pack seven words into three binary >digit words: > >one1,two1 := oddMaj(x1,x2,x3) >one2,two2 := oddMaj(x4,x5,x6) >ones,two3 := oddMaj(x7,one1,one2) >twos,four := oddMaj(two1,two2,two3) > >But already 11 pairs to pack 15 to 4. > >one1,two1 := oddMaj(x1,x2,x3) >one2,two2 := oddMaj(x4,x5,x6) >one3,two3 := oddMaj(x7,x8,x9) >one4,two4 := oddMaj(x10,x11,x12) >one5,two5 := oddMaj(x13,x14,x15) > >one6,two6 := oddMaj(one1,one2,one3) >ones,two7 := oddMaj(one4,one5,one6) > >two8,four1 := oddMaj(two1,two2,two3) >two9,four2 := oddMaj(two4,two5,two6) >twos,four3 := oddMaj(two7,two8,two9) >four,eight := oddMaj(four1,four2,four3) > >Hmm, 1,3,11 pairs for 2**2-1, 2**3-1 and 2**4-1 words... oups 1,4,11 of course >Too lazy to look for a general formula nPairs(N) now ;-( N nPairs N-nPairs 3 1 2 7 4 3 15 11 4 a first guess for 31 31 26 5 so may be for N = 2**n - 1 nPairs := N - n But to prove that (by induction?) definitely exceeds my math skills. Gerd
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