Binary Hex and Octal Calculator

Convert values across common programming number systems. Compare bases, operations, and signed bit ranges fast. Download neat reports for lessons, checks, and projects today.

Calculator Form


Arithmetic Options


Bitwise Options

Example Data Table

Decimal Binary Octal Hexadecimal Common use
10 1010 12 A Small counter value
45 101101 55 2D Byte level testing
255 11111111 377 FF Eight bit maximum
1024 10000000000 2000 400 Memory block size

Formula Used

Base to decimal:

Decimal value = dn × bn + dn-1 × bn-1 + ... + d0 × b0

For fractions, each digit after the point uses negative powers.

Fraction value = f1 × b-1 + f2 × b-2 + f3 × b-3

Decimal to another base:

Repeatedly divide the integer part by the target base. Read remainders from bottom to top. For fractions, repeatedly multiply by the target base.

Signed interpretation:

If the top bit is set, signed value = unsigned value - 2bits. Otherwise, signed value equals unsigned value.

Bitwise logic:

AND keeps shared 1 bits. OR keeps any 1 bit. XOR keeps different bits. NOT flips bits inside the selected width.

How to Use This Calculator

  1. Enter the value you want to convert.
  2. Select the source base that matches your input.
  3. Choose the target base for the main output.
  4. Set fraction precision and digit grouping if needed.
  5. Choose a signed bit width for two's complement checks.
  6. Enter operands if you need arithmetic or bitwise results.
  7. Press calculate to show results below the header.
  8. Use CSV or PDF buttons to save the same result.

Understanding Binary, Hex, and Octal Values

Number bases help computers store and display data. Decimal uses ten symbols. Binary uses two symbols. Octal uses eight symbols. Hexadecimal uses sixteen symbols. Each system represents the same quantity in a different written form.

Why This Calculator Helps

Manual conversion can be slow. It also becomes risky when fractions, signed ranges, and bitwise tasks appear. This calculator keeps those steps in one form. You can enter one value, select its base, and view every common output. You can also run arithmetic and integer bitwise logic.

Core Base Conversion Idea

Every digit has a place value. In base two, each place is a power of two. In base eight, each place is a power of eight. In base sixteen, each place is a power of sixteen. The calculator multiplies each digit by its place value. Then it adds the values to create a decimal result. From decimal, it divides or multiplies by the target base.

Arithmetic and Bitwise Use

Programmers often compare values in several bases. A memory mask may be easier in hex. A permission value may be easier in octal. A flag pattern may be clearer in binary. This tool lets you add, subtract, multiply, divide, and compare converted values. It also supports AND, OR, XOR, NOT, and shifts for integers.

Signed Number Checks

Signed interpretation matters in low level work. The same bit pattern can mean different values. With two's complement, the highest bit marks negative numbers. Choose a bit width to see the signed range. This helps when testing registers, packets, checksums, and embedded data.

Practical Uses

Students can learn place value without guessing. Developers can check masks before coding. Teachers can prepare examples quickly. Technicians can decode settings from device manuals. The export buttons save the current result as a simple report. Use them for homework, notes, or documentation.

Accuracy Tips

Remove spaces from pasted values. Pick the correct source base before submitting. For fractional values, increase precision when you need more digits. For bitwise results, remember that only the integer part is used. Very large numbers may exceed normal server integer limits. Keep critical engineering checks inside your approved toolchain. Always review unusual outputs before sharing final work.

FAQs

What is a binary number?

A binary number uses only 0 and 1. Computers use binary because digital circuits work with two main states, usually off and on.

What is a hexadecimal number?

A hexadecimal number uses sixteen symbols. It uses 0 to 9 and A to F. It is compact and common in programming.

What is an octal number?

An octal number uses digits from 0 to 7. It can represent binary groups neatly because each octal digit equals three binary bits.

Can this calculator handle fractions?

Yes. Enter a value with a point, such as 101.101. Then choose the correct source base and set the precision for output digits.

Why does hexadecimal use letters?

Decimal digits only provide ten symbols. Hexadecimal needs sixteen. Letters A through F represent values from ten through fifteen.

What does signed bit width mean?

Signed bit width controls two's complement interpretation. An 8 bit value, 16 bit value, and 32 bit value can show different signed meanings.

Do bitwise operations use fractions?

No. Bitwise logic works on integers. This calculator rounds operands to integer values, masks them by width, and then applies the selected operation.

What can I export?

You can export the current calculation result. The CSV file is useful for spreadsheets. The PDF file is useful for notes or reports.

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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.