Addition of two whole numbers

Description: This algorithm assumes that its input consists of two positive integers, each represented (using base 10 notation) by a sequence of characters which we will call "digits."

Specifically, we assume the first input number M is represented by the digits
m_j m_j-1 ··· m₂ m₁ m₀ for some j>=0
and likewise that the second input number N is repesented by digits
n_k n_k-1 ··· n₂ n₁ n₀ for some k>=0

The resulting sum will also be represented by a sequence of digits,
s_l s_l-1 ··· s₂ s₁ s₀ for some l>=0

Procedure:

Step 1. Assign index i the value 0.

Step 2. Assign carry the value 0.

Step 3. Let the value T equal that of carry.

Step 4. Unless i>j, add m_i to the value of T.

Step 5. Unless i>k, add n_i to the value of T.

Step 6. If T=0, stop the entire process.
If T<10, then let s_i equal T and let carry equal 0.
Otherwise, then let s_i equal (T-10) and let carry equal 1.

Step 7. Increment the value of i and go to step 3.

Assumed primitives:

Can determine whether a number is less than 10.

Can add a single digit to a number which is 10 or less.

Can subtract 10 from a number, if it is greater than or equal to 10.

Michael Goldwasser

Last modified: Wed Jan 16 23:52:45 CST 2002