Calculator
Formula Used
Binary to decimal: decimal = sum of each bit multiplied by 2 raised to its position.
Hexadecimal to decimal: decimal = sum of each digit multiplied by 16 raised to its position.
Decimal to binary: divide by 2 repeatedly and read remainders from last to first.
Decimal to hexadecimal: divide by 16 repeatedly and convert remainders above 9 into A through F.
Signed two's complement: signed value = unsigned value - 2 raised to word size when the sign bit is set.
How to Use This Calculator
- Enter a decimal, binary, or hexadecimal integer.
- Select the source base that matches your value.
- Choose a word size when signed interpretation matters.
- Turn on signed mode for binary or hexadecimal bit patterns.
- Select padding and grouping options for cleaner output.
- Press Calculate to show the result above the form.
- Use CSV or PDF buttons to save the same result.
Example Data Table
| Input | Source Base | Word Size | Signed Mode | Decimal Result | Binary Result | Hex Result |
|---|---|---|---|---|---|---|
| 255 | Decimal | 8 bits | Off | 255 | 1111 1111 | FF |
| 11111111 | Binary | 8 bits | On | -1 | 1111 1111 | FF |
| 7B | Hexadecimal | 16 bits | Off | 123 | 0000 0000 0111 1011 | 007B |
Number Systems in Maths
Decimal, binary, and hexadecimal are three views of the same value. Decimal is the system people use most. It uses ten symbols. Binary is the base used by digital circuits. It uses only zero and one. Hexadecimal is a compact way to write long binary patterns. It uses sixteen symbols, from zero to nine and A to F.
Why Conversion Matters
Conversions help students see structure inside data. A decimal total can become a binary register. A binary flag can become a short hex mask. A hex address can become a plain decimal number. These links are important in algebra, computing, networking, and electronics. They also make bitwise work easier.
Signed and Unsigned Values
Unsigned values never show a negative sign. They represent only zero and positive counts. Signed values can represent positive and negative numbers. Many systems use two's complement for signed storage. In that method, the highest bit acts as the sign indicator. A set highest bit can mean a negative value when a word size is selected.
Precision and Grouping
The calculator keeps the entered value as an integer string. It removes spaces and separators before checking the base. Then it converts through decimal form. Binary output can be padded to the chosen word size. It can also be grouped into nibbles or bytes. Grouping helps locate flags, masks, and storage boundaries.
Practical Study Use
Use this tool when checking homework, computer science notes, or embedded formulas. Enter the known value. Select its source base. Choose a word size when signed meaning matters. Read every converted result together. Check the bit length, hex digits, and byte estimate. These details show how much storage the value needs. They also reveal whether a chosen word size is suitable.
Common Mistakes to Avoid
Do not mix digit rules. A binary value cannot contain two. A hexadecimal value may contain letters. A decimal value should not contain A, B, or F. Also check leading zeros. They rarely change unsigned value. Yet they matter when a fixed word size is being studied. Always choose signed mode only when the stored pattern should be interpreted as negative-capable data. This keeps classroom answers consistent and easy to audit later.
FAQs
What does this calculator convert?
It converts integer values between decimal, binary, and hexadecimal. It also shows signed decimal, unsigned decimal, bit length, byte estimate, hex digits, one count, and parity.
Can I enter spaces in binary values?
Yes. Spaces, commas, and underscores are removed before validation. This lets you paste grouped binary or formatted decimal values without changing the real value.
What is signed mode?
Signed mode interprets binary or hexadecimal input as a two's complement bit pattern. It uses the chosen word size to decide whether the value is negative.
Does decimal input support negative numbers?
Yes. Negative decimal input is converted into a two's complement unsigned pattern using the selected word size. The value must fit that signed range.
Why choose a word size?
The word size defines the storage width. It controls padding, signed interpretation, and two's complement output for negative values.
What does binary grouping do?
Binary grouping adds spaces after every four or eight bits. It does not change the value. It only makes long binary output easier to read.
What is parity?
Parity tells whether the count of one bits is even or odd. It is useful when studying bit patterns, flags, and simple error-check ideas.
Can I download the result?
Yes. Use the CSV button for spreadsheet-friendly output. Use the PDF button for a compact printable summary of the calculated conversion.