Number Conversion

Hindu-Arabic numerals are written in the form a_na_n-1 ... a₁a₀ denoting, in number base r , the integer:

a_n · rⁿ + a_n-1 · r^n-1 + ... + a₁ · r¹ + a₀

Factoring this expression yields:

((...(( 0 · r + a_n ) · r + a_n-1 ) · r + ... ) · r + a₁) · r + a₀

This suggests an algorithm for converting a number expressed by digits d_nd_n-1 ... d₁d₀ to internal form in a left-to-right scan:

1. Initialize the accumulator, num = 0.

2. For each new digit, d_i , let a be the number denoted by d_i :
   In C, ( d_i - '0')
   In Lisp, (- (char-code d_i ) (char-code #\0))
   Then set num = num * r + a .

3. After all digits have been processed, num is the numeric value in internal form.