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19I16 IJAET0916949 v6 iss4 1615to1621.pdf


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International Journal of Advances in Engineering & Technology, Sept. 2013.
©IJAET
ISSN: 22311963
Case 4: If N1  odd; N2  odd, the output of results with all possible values of m1 , m2 , n1 , n2 are
considered under the criteria of Mixed Radix applicability with the help of a code generated in
MATLAB and obtained the possible values of N1 and N2 , along with N1  N2 .
% N1 is odd and N2 is odd
syms r1 r2 m1 m2 n1 n2 m0 n0 N1 N2;
x=1;
for m1=0:1:(r1-1)
for n1=0:1:(r1-1)
for m2=0:1:(r2-1)
for n2=0:1:(r2-1)
n0=1;
m0=1;
N1=r1.*r2.*m2+r1.*m1+m0;
N2=r1.*r2.*n2+r1.*n1+n0;
fprintf('\n m2 m1 m0
n2
n1
n0
N1
N2
N1xN2\n')
fprintf('\n %3.4f %3.4f %3.4f %3.4f %3.4f
%3.4f
%3.4f %3.4f
%3.4f\n',m2,m1,m0,n2,n1, n0, N1, N2, N1xN2)
x=x+1;
end
end
end
end
Multiplication of three natural numbers with mixed radix:

N1  r2 r1m2  r1m1  m0
N2  r2 r1n2  r1n1  n0
N3  r2 r1 p2  r1 p1  p0
N1  N2  N3   r2 r1m2  r1m1  m0    r2r1n2  r1n1  n0    r2r1 p2  r1 p1  p0 

(5)

log  N1  N2  N3   log   r2 r1m2  r1m1  m0    r2r1n2  r1n1  n0    r2r1 p2  r1 p1  p0  

log  N1  N 2  N3 
 log  r2 r1m2  r1m1  m0   log  r2 r1n2  r1n1  n0   log  r2 r1 p2  r1 p1  p0 

(6)

In the similar manner, if N1  even; N2  even; N3  even. The output of results with all possible
values of m1 , m2 , n1 , n2 , p1 , p2 are considered under the criteria of Mixed Radix applicability with the
help of a code generated in MATLAB and obtained the possible values of N1 , N2 and N3 , along
with N1  N2  N3 .
% N1 is even , N2 is even and N3 is even
syms r1 r2 m1 m2 n1 n2 m0 n0 p1 p2 p0 N1 N2 N3;
x=1;
for m1=0:1:(r1-1)
for n1=0:1:(r1-1)
for p1=0:1:(r1-1)
for m2=0:1:(r2-1)
for n2=0:1:(r2-1)
for p2=0:1:(r2-1)
n0=0;
m0=0;
p0=0;
N1=r1.*r2.*m2+r1.*m1+m0;
N2=r1.*r2.*n2+r1.*n1+n0;

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Vol. 6, Issue 4, pp. 1615-1621