How to resolve the algorithm Non-decimal radices/Convert step by step in the Mathematica/Wolfram Language programming language

Published on 22 June 2024 08:30 PM
#Wolfram

How to resolve the algorithm Non-decimal radices/Convert step by step in the Mathematica/Wolfram Language programming language

Table of Contents

Problem Statement

Number base conversion is when you express a stored integer in an integer base, such as in octal (base 8) or binary (base 2). It also is involved when you take a string representing a number in a given base and convert it to the stored integer form. Normally, a stored integer is in binary, but that's typically invisible to the user, who normally enters or sees stored integers as decimal.

Write a function (or identify the built-in function) which is passed a non-negative integer to convert, and another integer representing the base. It should return a string containing the digits of the resulting number, without leading zeros except for the number   0   itself. For the digits beyond 9, one should use the lowercase English alphabet, where the digit   a = 9+1,   b = a+1,   etc. For example:   the decimal number   26   expressed in base   16   would be   1a. Write a second function which is passed a string and an integer base, and it returns an integer representing that string interpreted in that base. The programs may be limited by the word size or other such constraint of a given language. There is no need to do error checking for negatives, bases less than 2, or inappropriate digits.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Non-decimal radices/Convert step by step in the Mathematica/Wolfram Language programming language

The provided code snippet written in Wolfram programming language performs the following tasks:

  1. IntegerString[26, 16]: This line converts the integer 26 to a string representation in base 16 (hexadecimal). Hexadecimal uses the digits 0-9 and the letters A-F to represent numbers. In this case, 26 in base 10 is represented as "1a" in base 16.

  2. FromDigits["1a", 16]): This line creates an integer from a string of digits in a specified base. Here, the string "1a" is converted from base 16 (hexadecimal) to its integer equivalent, which is 26 in base 10.

Explanation:

The IntegerString function takes two arguments: the integer to be converted and the base to use for the representation. The FromDigits function takes two arguments: the string of digits and the base to use for the conversion.

In the given code, the IntegerString function converts the integer 26 to its hexadecimal representation, which is "1a". Then, the FromDigits function converts the hexadecimal string "1a" back to its integer equivalent, which is 26.

This code essentially performs a conversion between base 10 (decimal) and base 16 (hexadecimal) and verifies that the conversion round-trips correctly.

Source code in the wolfram programming language

IntegerString[26,16]
FromDigits["1a", 16])

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