Converting and Adding Binary Numbers

[jainamichelle]

Hi all,

I need help writing a program, using Fortran 90, to convert numerical values into binary then add them.

I'm able to convert numbers into binary, but I'm having difficulty adding two binary numbers. All I know is that I have to use a loop to add corresponding digits, starting with the lower digit, and the carry digits.

So far I have...

program ItAllAddsUp
implicit none

integer:: x=13, y=23, I, J,
integer:: Array1(8)
integer:: Array2(8)
integer:: Array3(8)

!Array for x value
do I=8, 1, -1
Array1(I)=MOD(x, 2)
x=x/2
end do

!Array for y value
Do J=8, 1, -1
Array2(J)=MOD(y, 2)
y=y/2

end do
end program ItAllAddsUp


----
Any help would be much appreciated.

Thank you very much

 

[FJacq]

Not very difficult if you program the reverse transformation :
- translating the two "binary" arrays into integers
- adding the integers
- transforming again integer result into a binary array

The corresponding programming is provided at the end. But I have several additional remarks :

- why doing a loop from 8 to 1 ? the array should be dimensioned to 32 because a normal integer value is coded on 32 bits (even on most 64 bits architectures).

- why do you want to add these binary arrays ? I ask for that question because I generally use a similar technique to register up to 32 logical options into a single integer. So I never "add" these binary representations but compute OR or XOR or AND bit wise operations.

- you should examine carefully intrinsic bit manipulation functions of FORTRAN-2003 like BTEST, IAND, IBCLR, IBITS, IBSET, IEOR, IOR, ISHFT, MVBITS, NOT. For instance, BTEST(value,position) returns a logical value indicating if the bit at a given position is equal to 0 (false) or 1 (true). The position starts from 0 to 31 (it corresponds to the exponent of 2). So your loop from 8 to 1 should be replaced by a loop from 0 to 31 to match the FORTRAN integer model and the arrays could be dimensioned (0:31).

Example to solve your initial request with arrays declared DIMENSION(32) :

module binary

  implicit none
  
  contains
  
  function integer2binary(i) result(b)
    integer,intent(in) :: i
    integer :: b(32)
    integer k,j
    b=0
    j=i
    do k=1,size(b)
      b(k)=mod(j,2)
      j=j/2
    enddo
  end function
  
  function binary2integer(b) result(i)
    integer :: i
    integer,intent(in) :: b(:)
    integer k,j
    i=0
    j=1
    do k=1,size(b)
      i=i+b(k)*j
      j=j+j
    enddo
  end function
  
  function sum(b1,b2) result(b3)
    integer,intent(in) :: b1(:),b2(:)
    integer :: b3(32)
    b3=integer2binary(binary2integer(b1)+binary2integer(b2))
  end function
  
end module

program test
  use binary
  integer :: i=13,j=23,k
  integer,dimension(32) :: bi,bj,bk
  bi=integer2binary(i)
  write(*,'(32i1)') bi
  write(*,*) binary2integer(bi)
  bj=integer2binary(j)
  bk=sum(bi,bj)
  write(*,*) i+j,binary2integer(bk)
end program