Question

Write the Right to Left binary exponentiation algorithm. Demonstrate the use of this algorithm to compute the value of 523. Show all steps of the computation. Explain the worst-case complexity of this algorithm.

18 Feb 2026
Answer :
Word Count : 578
Binary exponentiation is an efficient method to compute large powers of a number by reducing the number of multiplications using the binary representation of the exponent. The Right to Left binary exponentiation algorithm processes the bits of the exponent starting from the least significant bit and moves towards the most significant bit. It repeatedly squares the base and multiplies it to the result whenever the current bit of the exponent is 1. The Right to Left binary exponentiation algorithm can be written as follows: Algorithm RightToLeftBinaryExponentiation(a, n) Input: Base a, non-negative integer exponent n Output: Value of a^n 1. result ← 1 2. while n > 0 do 3. ``` if n mod 2 = 1 then ``` 4. ``` result ← result × a ``` 5. ``` end if ``` 6. ``` a ← a × a ``` 7. ``` n ← floor(n / 2) ``` 8. end while 9. return result This algorithm works by examining each binary digit of n. If the current bit is 1, the current value of a is multiplied into the result. Then the base is squared and the exponent is divided by 2 using integer division, effectively shifting its binary representation to the right.
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