Binary And Hexadecimal Calculator

Convert binary and hexadecimal numbers with detailed steps. Compare arithmetic, bitwise logic, and shifts easily. Export clean results for study and coding tasks today.

Calculator Input

Example Data Table

Input A Base A Input B Base B Operation Decimal Result Hex Result
1010 2 F 16 Add 25 19
FF 16 15 10 AND 15 F
10000000 2 2 10 Right Shift 32 20

Formula Used

For base conversion, each digit is multiplied by its positional weight.

Decimal value = dn × bn + dn-1 × bn-1 + ... + d0.

Hexadecimal groups match binary groups because one hex digit equals four binary digits.

Arithmetic uses converted decimal values first, then formats the result back into supported bases.

Bitwise operations use the selected bit length, then apply AND, OR, XOR, NOT, or shifts with a mask.

How To Use This Calculator

  1. Enter operand A and choose its base.
  2. Select the operation you want to run.
  3. Enter operand B when the operation needs two values.
  4. Choose the bit length for bitwise logic and signed views.
  5. Press Calculate to show the answer below the header.
  6. Use CSV or PDF buttons to export the calculated result.

Binary And Hexadecimal Calculator Guide

What This Calculator Does

A binary and hexadecimal calculator helps you study digital values faster. It converts numbers between base two, base ten, base eight, and base sixteen. It also handles arithmetic and bitwise logic. These features are useful for computer science, electronics, networking, and discrete math. You can compare each result with steps, so the process is easier to verify.

Why Number Bases Matter

Decimal numbers use ten symbols. Binary uses only zero and one. Hexadecimal uses sixteen symbols, from zero to nine and A to F. Computers store data in binary, yet long binary strings are hard to read. Hexadecimal shortens those strings. Four binary digits match one hexadecimal digit. This makes memory addresses, colors, masks, opcodes, and packets easier to inspect.

Useful Operations

The calculator can add, subtract, multiply, and divide values entered in different bases. It also supports AND, OR, XOR, NOT, left shift, and right shift. Arithmetic operations work on decimal conversions first. Then the tool formats the final answer in each supported base. Bitwise operations compare bits directly after both values are normalized.

Reading The Results

Every result includes decimal, binary, hexadecimal, and octal forms. Signed decimal is also shown. This helps when a value represents two's complement data. The bit length field controls how NOT and signed values are interpreted. Use eight bits for bytes, sixteen bits for words, and thirty two bits for common registers.

Good Input Practice

Enter only valid symbols for the selected base. Binary input accepts zero and one. Hexadecimal accepts numbers and letters A through F. Spacing is allowed for readability, but extra prefixes are removed automatically. If a value is invalid, the page explains the error before any result is shown.

Study And Export Use

Use the example table to test known values. Then enter your own operands. Download the result as CSV for spreadsheets. Download the PDF summary for reports or class notes. These exports make the calculator practical for assignments, tutorials, and code documentation.

Common Learning Tips

Check small examples before large ones. Try 1010, FF, and 255. Notice how the same quantity changes shape, while its value stays stable across every base. This builds conversion confidence for daily practice.

FAQs

What is a binary number?

A binary number uses only 0 and 1. It is base two. Computers use binary to store and process data through electrical states.

What is a hexadecimal number?

A hexadecimal number is base sixteen. It uses digits 0 to 9 and letters A to F. It is a compact way to show binary data.

Can I add binary and hexadecimal values together?

Yes. Choose each input base, enter both values, and select addition. The calculator converts both inputs to decimal before calculating the final result.

Why does the calculator show octal too?

Octal is another common base in computing. It groups binary digits in threes. Showing octal gives a wider comparison for study and debugging.

How does bitwise AND work?

Bitwise AND compares matching bits. A result bit becomes 1 only when both input bits are 1. Otherwise, that result bit becomes 0.

What does bit length control?

Bit length controls masks, NOT results, shifts, and signed interpretation. Select 8, 16, or 32 bits based on the data size you need.

Can I download the result?

Yes. After calculation, use the CSV button for spreadsheet data. Use the PDF button for a simple printable report.

Why does invalid input show an error?

Each base accepts only certain digits. Binary cannot use 2. Hexadecimal cannot use letters beyond F. The error helps you correct the value.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.