Uniform random number generation in Computer

Let's, have a generator, Ui(R_max+1), to generate uniform random integer r ∈ [0...R_max].
We can construct Ui(N) in following way,

Ui(N) =

1. Range = R_max - ( R_max )mod N
2. do
1. r = U(R_max+1);
3. while( r  ≥  Range );
4. Return(r);

Similarly, we can further construct a real random number generator Ur(N), which generates random real r ∈ [0,1]. using  Ui(N).

Ur(N) = (N-1)/Ui(N);

Ber(p) = ( Ur(N) ≤ p ) + (Ur(N) > p) ;
Binomial(n,p) =

1. y = 0
2. for(i = 0; i < n; i = i + 1)
1. y = y + Ber(p)
3. Return y