Base Conversion Calculator
Base Conversion Calculator
Conversion Breakdown
| Input | 255 (base 10 · Decimal) |
| Decimal (base 10) | 255 |
| Binary (base 2) | 1111 1111 |
| Octal (base 8) | 377 |
| Hexadecimal (base 16) | 0xFF |
| Bit Width | 8 bits |
Digit Count by Base
Summary Statistics
What Is a Base Conversion Calculator?
A base conversion calculator translates a number from one numeral system to another. Computers work in binary (base 2), where every value is a sequence of 0s and 1s, but humans usually read decimal (base 10). Octal (base 8) and hexadecimal (base 16) are compact shorthands that map cleanly onto groups of binary digits, which is why they appear constantly in programming, memory addresses, color codes, and low-level debugging. This tool takes a value in any of these four bases and instantly shows its equivalent in all the others, so you never have to convert by hand.
How Base Conversion Works
Converting from any base to decimal uses positional notation: each digit is multiplied by its base raised to the position's power, then summed. Converting decimal to another base uses repeated division — divide by 2 for binary, 8 for octal, or 16 for hexadecimal, and collect the remainders in reverse. For signed values, this calculator uses two's complement within a chosen bit width: negative numbers are stored by inverting the bits of the magnitude and adding one. Bit width also pads the binary output to a fixed size such as 8, 16, 32, or 64 bits, matching common data types used in software.
Understanding Your Results
The primary card shows your value in binary, with decimal, octal, and hexadecimal equivalents beneath it. The three-stat bar summarizes the decimal, octal, and hex forms at a glance, while the breakdown table lists every representation plus the active bit width. The digit-count chart compares how many digits the same number needs in each base, illustrating why hexadecimal is so compact for large values. Use the Advanced Options to enable two's complement for negative numbers, adjust bit width for padding, and toggle bit grouping to add spaces every four binary digits for easier reading.
Frequently Asked Questions
Related Calculators
Home Loan Calculator
Calculate home loan EMI, total interest, and amortization schedule.
Auto Loan Calculator
Detailed auto loan with trade-in, taxes, fees, and amortization.
Bike Loan Calculator
Calculate bike loan EMI, total cost, and repayment breakdown.
Boat Loan Calculator
Estimate boat financing payments, interest, and amortization.
Student Loan Calculator
Calculate student loan payments with income-driven repayment plans.
Gold Loan Calculator
Calculate gold loan amount based on gold weight, purity, and LTV ratio.
USDA Loan Calculator
Calculate USDA loan payments with guarantee fee and income eligibility.
Loan Against Property Calculator
Calculate LAP EMI based on property value and loan-to-value ratio.