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How does a calculator work?

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Quick answer

A calculator turns each key press into a binary number, then uses a logic chip or stored program to add, subtract, multiply, or divide those numbers. It converts the binary result back into decimal digits and shows them on a screen.

A calculator converts each key press into a binary number, then uses a pre-built logic circuit or a stored program to perform arithmetic on those numbers. The result is decoded and shown on the display as decimal digits.

Step by step

  1. You press a key, completing a circuit that sends a unique electrical signal to the calculator's processor.
  2. The processor converts that signal into a binary number, such as 0 for the digit 0 and 1 for the digit 1.
  3. The processor stores the first number and the chosen operation in its memory.
  4. When you press equals, the processor performs the operation using binary addition or repeated addition.
  5. The binary result is converted into decimal digits by a decoder chip.
  6. The decoder drives the display segments to show the final number.

Key things to understand

  1. Each key press sends a unique electrical signal to the calculator's processor.
  2. The processor converts that signal into a binary number using a keypad encoder.
  3. A logic unit performs addition, subtraction, multiplication, or division on binary numbers.
  4. The binary result is converted back to decimal digits by a display decoder.
  5. The final digits are shown on a liquid-crystal or light-emitting-diode display.

Labelled diagram

  1. Keypad

    Each key connects a row and column wire, sending a unique signal to the processor.

  2. Processor

    Converts the signal to binary, stores numbers, and selects the operation.

  3. Logic unit

    Performs binary addition, subtraction, multiplication, or division on the stored numbers.

  4. Decoder

    Converts the binary result into signals for each decimal digit.

  5. Display

    Liquid-crystal or light-emitting-diode segments light up to show the digits.

From key press to displayed answer

Real-world examples

  • A pocket calculator from Casio or Texas Instruments uses a single microchip to handle keypad input, arithmetic, and display output.
  • A smartphone calculator app runs as software on the phone's main processor, using the same binary arithmetic but with a touchscreen interface.
  • A graphing calculator like the TI-84 uses a programmable processor to evaluate expressions with parentheses, exponents, and trigonometric functions.
  • An adding machine used in shops prints results on paper tape, using mechanical wheels or early electronic circuits to count.

Common mistake

✗ Myth: A calculator thinks like a human and understands numbers.

✓ Fact: A calculator has no understanding; it follows fixed electrical pathways or stored instructions that manipulate binary codes. It performs operations mechanically, without any awareness of what the numbers represent.

People also ask

How does a calculator add numbers?
A calculator adds by using binary logic gates that combine two binary numbers bit by bit. It starts from the rightmost bit, adds each pair, and carries a 1 to the next position when the sum is 2 or more. The final binary result is then converted to decimal for the display.
What is inside a calculator?
Inside a basic calculator you find a small microchip (the processor), a keypad with conductive contacts, a liquid-crystal display, a solar cell or button battery, and a plastic case. Scientific calculators add more memory and a more powerful processor to handle complex functions.
Why do calculators use binary?
Calculators use binary because electronic circuits have two reliable states: on and off. Representing numbers as 0s and 1s lets the calculator use simple, fast logic gates for arithmetic. Decimal numbers would require ten distinct voltage levels, which are harder to detect accurately.
How does a calculator know which operation to do?
The operation key you press sets a temporary code in the calculator's memory. When you press equals, the processor reads that code and sends the stored numbers to the correct logic circuit for that operation.
Why do some calculators use batteries and others plug in?
Basic calculators use tiny amounts of power, so small solar cells or button batteries last for years. More powerful graphing calculators need more energy for larger screens and faster processors, so they often use rechargeable batteries or adapters.
Can a calculator make mistakes?
A working calculator's arithmetic is exact for the numbers it can represent. Errors come from the user pressing wrong keys, from rounding very large or very small numbers, or from a hardware fault.
What is the difference between a basic and a scientific calculator?
A basic calculator only does arithmetic. A scientific calculator also handles trigonometry, logarithms, powers, and roots by using more complex internal programs and additional function keys.

Part of the guide: Everyday Machines →