For the finite ring R2 = {00000000, 00000001, ..., 11111111} find: 11010111⊖10101010 = N2

Question

Question

engineering Computer-Science

Answer 1

Answer #1

The finite Ring has elements that are finite in number
in other words, the elements are not infinite
they are finite and countable with in a set limit
The Ring can accommodate binary operations + and . those satisfy the distributive laws
For example, for all p,q, and r that belongs to Real set R,
we can say that (p+q).r = (p.r + q.r)
and also
p.(q+r) = p.q + p.r
and also
q.(p+r) = q.p + q.r
which is the same as
(p+r).q = p.q + r.q
The finite field can make a legitimate example of a finite ring
Given a collection of i items, beginning with i = zero, we can make a collection of rings with these i items as follows:
a,a,b,b,k,b,d,b,zz,k,d,b,v,b,d,d,cia,b,v,b,v,d,d,b,…..
The standard application of finite rings is in terms of the enumerations
for each item i that belongs to the ring R, there will be an integer m greater than unity in such a way that i ^ m = i – in that case the ring R satisfies the commutative property
as long as there are prime numbers p , and positive integers m, there will be finite fields with a total element count of p^n elements
Tow finite elements will satisfy the isomorphic property if their order are the same
Hence,
11010111 q 10101010 = N2

Answer 2

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