How do engineering calculators work? A look inside their brains

At first glance, an engineering calculator, with its small buttons and simple display, seems like an ordinary tool; but behind this simple appearance lies a complex world of mathematics, digital logic, and advanced algorithms that provide you with the most accurate calculations with just a few short touches.

In this article, we will take a journey inside the brain of this smart device and see how a small machine performs mathematical operations with high accuracy and amazing speed.

✅ What is the brain of a calculator?

At the heart of every calculator, especially engineering models, is a smart chip, which usually includes a low-power processor and a lightweight memory. This processor processes all the mathematical operations and converts the inputs into understandable results. That’s why the calculator can calculate quickly and accurately, even without an internet connection and with just a few small batteries.

Today, with the advancement of technology, even calculators have become smarter; an example of this is the PayVAS1 calculator, designed by Navosh Aria Intelligent Processing Company. This calculator, with the ability to connect directly to bank POS, has made the sales process simpler, faster, and more cost-effective for shopkeepers.

🔢 How does a calculator perform complex operations?

Every time a button is pressed on a calculator, the information is converted into the machine’s internal language and then processed. In engineering calculators, functions such as sine, logarithm, power, root, matrix, and even complex numbers can be calculated. This calculation is done using algorithms such as Taylor series, stack algorithm, or infix-to-postfix conversion.
For example, when you type:
`sin(30)`
This input is converted by the processor to its numerical equivalent (i.e. 0.5), which is the result of a complex mathematical function.

Main brands

When it comes to engineering calculators, a few reputable global brands are always at the top of the list. These companies have earned the trust of students, engineers, and even university professors for years by producing accurate, durable, and innovative devices:

Casio: One of the most famous scientific and engineering calculator brands in the world, offering various models such as the fx-991EX or ClassWiz.

Texas Instruments (TI): A leader in the design of graphic and programmable calculators, particularly for use in advanced mathematics and academic education.

Navosh: Navosh Aria Intelligent Processing Company has designed a calculator for the first time in Iran that can be directly connected to a POS device. This calculator works instead of a PIN pad or cash register and creates high added value for guilds and stores at a reasonable price. This product is an innovative example of Iranian-made financial technology (FinTech) and can play an important role in the future of smart payment tools.

How does memory work in a calculator?

A calculator, especially an engineering type, is not just a tool for performing instantaneous calculations; it can also store values to be used again in later calculations. This is done by means of internal memory. Now let’s see how this memory works and what capabilities it has.

🔹 simple memory (M+, M-, MR, MC)

Calculators often have a basic memory that works with the following buttons:

M+ (Memory Plus): Adds the current number to memory.

M- (Memory Minus): Subtracts the current number from the value stored in memory.

MR (Memory Recall): Displays the stored value.

MC (Memory Clear): Clears memory.

Example: Suppose you enter the number 100 and press M+. Now if you enter the number 50 and press M+ again, the memory will hold the value 150. You can see it with MR.

🔹 Multiple memories (STO and RCL)

In more advanced engineering calculators (such as the Casio fx-991 or TI), several different values can be stored in separate memories.
STO (Store): Stores the current number in a specific memory. Usually accompanied by a letter like A, B, C, D.
Example: `5 → STO → A` means store the number 5 in memory A.
RCL (Recall): Recalls the value stored in a specific memory.
Example: `RCL → A` means retrieve the value in memory A.
These types of memories are very useful for solving long equations or multi-step calculations.

🔹 Temporary memory (Ans or Answer)

The Ans or “previous answer” button is found on many calculators and holds the last calculated result.
For example:
12 × 4 = 48
Then you enter:
Ans + 6 = 54

This feature helps you avoid having to retype numbers all the time.

🔹 RAM memory and permanent memory

In a programmable or graphing engineering calculator, such as the TI-84 or Casio ClassPad, there are two types of memory: RAM: For temporary storage of programs, calculation steps, and intermediate values. It may be erased when the device is turned off.
ROM or Flash Memory: For storing programs, formulas, or data that must be permanent.

Why is memory important in a calculator?

Memory in a calculator is not just an accessory; it is one of the most key features for increasing the accuracy, speed, and efficiency of performing complex calculations. Especially in engineering and scientific calculators, memory is like a faithful assistant that holds important numbers and results for reuse.

Below, we examine some clear reasons why memory is important in a calculator:

🔹 1. Prevent re-entering numbers

Sometimes in a long calculation, you need to use a specific number (such as a resistor value, coefficient, or physical constant) multiple times. Instead of entering it repeatedly, you can store it in memory once and recall it each time with a simple button press.
Example: Storing the number 9.81 (gravitational acceleration) in memory A and using it repeatedly in physics calculations.

🔹 2. Reduce the possibility of error

When you retype numbers, even a small mistake can ruin the entire calculation. Using memory eliminates this human error and delivers more accurate calculations.

🔹 3. Accelerate multi-step calculations

In many engineering and mathematical problems, calculations must be performed step by step. Memory helps you store intermediate results and use them in later steps, without having to write or jot them down on paper.
Example: In calculating a circuit, first voltage, then current, then power – each step requires using the value of the previous step.

🔹 4. Application in solving equations

In some models, the memory can hold multiple variables (such as A, B, C) and use them in solving multi-variable equations or even numerical programming.
Example: Solving a quadratic equation using the general formula

x = (-B ± √(B² – 4AC)) / 2A

If you memorize A, B, C, you can just enter the formula and use it over and over again.

🔹 5. Ease of review and repetition

When your calculator holds the previous result in memory (Ans), you can easily use it to test or repeat a previous calculation, without having to calculate again.

🔹 6. Save custom programs or functions (in advanced models)

In programmable or graphing calculators, memory is used to store calculation codes, arbitrary functions, and analytical data. This means that the calculator becomes a semi-intelligent tool.
Example: Save a program to calculate the volume of geometric objects or calculate compound interest rates

Why are calculators still important?

In the age of smartphones and apps, the physical calculator still holds its place in many professional and educational environments. The reasons are:
High accuracy in calculations.
Easy to use in emergencies or exams.
Independence from electricity or the internet.
Legal compliance in exams; Most standardized exams, such as the entrance exam or international exams, do not allow phones, but the use of engineering calculators is allowed.

Types of engineering calculators

There is not just one model of engineering calculator; there are many different types on the market depending on the level of use, features, and manufacturer brand. Understanding these models helps students, engineers, and even teachers make the best choice based on their needs.

Below we will learn about the types of engineering calculators:

(Basic Scientific Calculators)

Suitable for: High school students, college entrance exam candidates, and first-year students

Capabilities:

• Performing four main actions
• Trigonometric functions (sin, cos, tan and their inverses)
• Logarithms and powers
• Percentage and factorial calculation
• Simple memory and Ans button
• Calculating numbers in base 10
• Examples:
  Casio fx-82MS
  Canon F-789SGA
  Sharp EL-501X

✅ Distinctive feature: Easy to operate, low price, suitable for tests

Advanced Scientific Calculators

Suitable for: Engineering, Math, Physics and Technical Students
Features:

• All features of the base model +
• Calculation with numeric bases (binary, hexadecimal, etc.)
• Matrix, vector and complex number calculations
• Equation Solver
• Multi-line display or Natural Display
• Storing multiple variables in memory
• Statistical performance and regression
• Examples:
  Casio fx-991ES Plus
  Casio fx-570EX (ClassWiz)
  Sharp EL-W506X

✅ Distinctive feature: Suitable for university, with functionality very close to a programmable calculator

Programmable Calculators

Suitable for: Professional engineers, graduate students, numerical programmers

Capabilities:

• Programming in a special language (usually similar to BASIC)
• Save and execute multiple calculation steps
• Plotting complex functions
• User-defined functions can be saved.
• Complex numerical calculations, such as numerical integration or solving equations
• Simple differential
• Examples:
  Casio fx-5800P
  Sharp EL-5200
  HP 35s

✅ Outstanding feature: customizable for specific needs, suitable for numerical projects

Graphing Calculators

Suitable for: researchers, professors, students of applied mathematics, differential equations, analytic geometry

Capabilities:

• Graphing two-dimensional and three-dimensional functions
• Display variables and graphs on a large screen
• Internal memory for storing data and applications
• Possibility of connecting to a computer or data projector
• Specific programming language (such as TI-BASIC or Python)
• Examples:
  TI-84 Plus
  TI-Nspire CX II
  Casio fx-CG50

✅ Notable feature: Ability to graph and visually analyze functions – usually not allowed on exams

Combined calculator with payment system (like PayVAS1)

Suitable for: Shopkeepers, small businesses

Capabilities:

• Basic mathematical calculations
• Direct connection to POS device
• Sending the final calculated number to the card reader
• Cost-effective alternative to a store checkout
• Example: PayVAS1 manufactured by Navosh Aria Company

✅ Distinctive feature: Combination of calculator and POS to facilitate sales operations

What will be the future of calculators?

Although calculator apps are improving day by day, physical calculators still hold a special place in many universities and prestigious scientific environments. Some new models even have the ability to connect to a computer, program, and store data.

Small brain with big function

An engineering calculator is a tool that, despite its small size, has complex and precise functionality. Through a combination of intelligent hardware, optimized software, and advanced algorithms, calculators allow us to perform the most complex calculations in real time.