Need help please Magnitude comparator 3 bit super Kmap for G

Need help please

Magnitude comparator 3 bit super K-map for GT(u,v) 0 0 12 8 32 6 45 35 39 14 10 1 34 46 42 52 60 8 24 9 25 27 48 49 51 20 61 63 59 62 58 21 19 23 1 18 1 50 54 2m(4,8,9,12,13,14,16,17,18,19,20,21,22,23,24,25,26,27,28, 29,30,31,52,56,57,60,61,62) Show that GT(u,v) -u,v+(u,tv)uv,+ (u,tV)(u,+v)u,v 1 1 0 0

Solution

the both equation are same interms of functionality.But

(U+V\') boolean equation ensure U and V are same or U is greater than V

.let we check,when U=0 and V=0 then U+V\'=0+1=1;here U and V are same we got 1 as output

when, U=1 and V=1 then U+V\'=1+0=1;here U and V are same we got 1 as output

when U=0 and V=1 then U+V\'=0+0=0;here U is less than V we got 0 as output

when U=1 and V=0 then U+V\'=1+1=1;here  U is greater than V we got 0 as output.

(U2+V\'2) gives the information either U2>V2 or U2=V2. to ensure U is greater we need to cheeck next bit U1 and V1

using U1V1\' boolean equation. which ensure U>V.

In another equation x is used to check a and b bit are equal ,if both are equal x=1,else x=0.

a2b2\'+x2a1b1\'+x2x1a0b0\' in this term

a2b2\'=1 means a2 is greater,no need to check further bits and we can say a>b;

x2a1b1\'=1,means a2=b2,and a1>b1,no need to check further bits and we can say a>b;

x2x1a0b0\'=1 means , a2=b2,and a0>b0, we can say a>b;