Programmer Calculator

About the Programmer Calculator

A programmer's calculator that converts a whole number between binary, octal, decimal and hexadecimal bases, and shows bitwise representations.

How to use this calculator

1. Enter the integer you want to convert, such as 42.
2. Choose the number system it starts in, for example decimal.
3. Select the output base you want, such as binary, octal, or hexadecimal.
4. Read the converted value and the step-by-step conversion shown by the calculator.

The formula explained

This tool converts one whole number from a chosen base into another base. It computes the same value in a different numeral system, not a different number.

• n = the integer being converted
• b = the base or number system, such as 2, 8, 10, or 16

Step by step method

1. Start with the given number in its original base.
2. Convert it to a decimal value if needed, because decimal is the easiest bridge between bases.
3. Rewrite that decimal value in the new base by repeated division and recording remainders.

Worked example

Problem. Convert 42 from decimal to binary, octal, and hexadecimal.

1. Decimal 42 stays 42 in base 10.
2. For binary, divide by 2 repeatedly: 42, 21 r0, 10 r1, 5 r0, 2 r1, 1 r0, so the binary form is 101010.
3. For octal, divide by 8: 42, 5 r2, 0 r5, so the octal form is 52. For hexadecimal, divide by 16: 42, 2 r10, and remainder 10 is A, so the hexadecimal form is 2A.

Tips and common mistakes

• Remember that hexadecimal uses A through F for values 10 through 15.
• A common mistake is mixing up the base, so check whether the input number is binary, octal, decimal, or hexadecimal before converting.

Frequently asked questions