... of Decimal of any size into ... 1:The Binary of any decimal ... can be ... as ... where, k is a positive integer. r is such that 2pow(r) is a nu
Conversion of Decimal of any size into Binary Statement 1: The Binary of any decimal 2pow(n)+k can be formatted as 1(n−r)zeroesB(k).
where, k is a positive integer. r is such that 2pow(r) is a number greater than and nearest to k. B(k) is the binary of k. Statement 2: The Binary of any decimal 2pow(n)−k can be formatted as (n−(r+1))onesB(p). where, k is a positive integer. r is such that 2pow(r) is greater than and nearest to k. p=(2pow(r+1))−k. B(p) is the binary of p.
For Example: To find the binary of 2055: 2055=(2pow(11))+7; here, n=11; k=7;so r=3(since 2pow(r) ie., 2pow(3)=8 in nearer and greater than k ie., 7) also B(k)=B(7)=111. Therefore, binary of 2055 is of the form 1(11−7)zeroes111. The above result is obtained using statement 1.
To find the binary of 4090: 4090=2pow(12)−6. Here, n=12; k=6;so r=3(since 2pow(r) ie., 2pow(3)=8 in nearer and greater than kie.,7) also,p=2pow(3)+1−6=10.B(p)=1010; Therefore, binary of 4090is of the form 12(3+1)ones B(10). The above result is obtained using statement 2.
