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Programming a Calculator To Solve Complex Numerical Expressions
Calculators have much in common with compilers and interpreters. Explore the details with code examples and algorithms explanations
Calculators, we often use them thoughtlessly without caring about how they work under the hood. Programming a calculator may seem a simple task — just evaluate the given expression — but there’s much more than that involved. You may find these pieces of software much similar to a compiler or an interpreter.
This article will first provide an overview of the inner working of a calculator program. I’ll then focus on the fine details, including a complete line-by-line code walkthrough. I will also leave a link to the GitHub repository at the end of the article.
Understanding the Mathematical Expression
A mathematical expression can be defined as a sequence of syntagmas such as numbers, mathematical operators, parentheses, and functions. In the case of calculators, expressions are provided as a string like this: "3 + 5 * 2" . Given a string input, the calculator has to recognize and divide the expression into its basic components in order to “understand” it. This process is also known as tokenization or lexical analysis, and it’s also what compilers and interpreters do with your source code to be able to analyze it.
For instance, for the input string "3 + 5 * 2" the calculator must recognize the tokens it’s composed of: the numbers 3, 5, and 2 and the mathematical operators +and *. In order to do that, it has to iterate over every character of the expression and check which type of syntagm it’s dealing with. I’ll explain the details of this process later.
Evaluating the Mathematical Expression
Only after the given expression is divided into basic tokens, the calculator is actually able to work out what it’s being requested to solve. At this point, the mathematical interpreter can look for the operator with the highest priority and evaluate its operation. The priority of an operator, also known as operator precedence, follows the basic rules we’re all familiar with: operations inside parentheses come…
