Binary Converter
Instantly convert binary with our free converter. See conversion tables, formulas, and step-by-step explanations. Free to use with no signup required.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator
Binary Converter
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Formula: Decimal = sum of (bit x 2^position)
Worked example โ 200 = 11001000 (binary) = 310 (octal) = C8 (hex)
Formula
Decimal = sum of (bit x 2^position)
Each binary digit (bit) represents a power of 2 based on its position from right to left, starting at position 0. To convert binary to decimal, multiply each bit by 2 raised to its position power and sum the results. For example, binary 1010 = 1x8 + 0x4 + 1x2 + 0x1 = 10.
Worked Examples
Example 1: Decimal 200 to Binary
Problem:Convert decimal number 200 to binary.
Solution:200 / 2 = 100 r 0 100 / 2 = 50 r 0 50 / 2 = 25 r 0 25 / 2 = 12 r 1 12 / 2 = 6 r 0 6 / 2 = 3 r 0 3 / 2 = 1 r 1 1 / 2 = 0 r 1 Binary: 11001000
Result:200 = 11001000 (binary) = 310 (octal) = C8 (hex)
Example 2: Binary 10110 to Other Bases
Problem:Convert binary 10110 to decimal, octal, and hexadecimal.
Solution:Decimal: 1x16 + 0x8 + 1x4 + 1x2 + 0x1 = 22 Octal: 22 / 8 = 2 r 6 -> 26 Hex: 22 / 16 = 1 r 6 -> 16
Result:10110 (binary) = 22 (decimal) = 26 (octal) = 16 (hex)
Frequently Asked Questions
What is binary and why do computers use it?
Binary is a base-2 number system that uses only two digits: 0 and 1. Computers use binary because their fundamental building blocks (transistors) have two states: on and off. These two states map perfectly to the binary digits 1 and 0. Every piece of data a computer processes, from text to images to programs, is ultimately represented as sequences of binary digits (bits). This simplicity makes digital circuits reliable and efficient to manufacture.
How do I convert decimal to binary?
To convert a decimal number to binary, repeatedly divide the number by 2 and record the remainder. Continue until the quotient is 0. Then read the remainders from bottom to top. For example, to convert 13: 13/2 = 6 remainder 1, 6/2 = 3 remainder 0, 3/2 = 1 remainder 1, 1/2 = 0 remainder 1. Reading bottom to top gives 1101. So decimal 13 equals binary 1101.
What is the difference between binary, octal, and hexadecimal?
These are all positional number systems with different bases. Binary is base 2 (digits 0-1), octal is base 8 (digits 0-7), and hexadecimal is base 16 (digits 0-9 plus A-F). They are related by powers of 2: each octal digit corresponds to exactly 3 binary bits, and each hexadecimal digit corresponds to exactly 4 binary bits. This relationship makes conversions between them straightforward and is why all three are commonly used in computing.
How do I convert binary to hexadecimal without going through decimal?
Group the binary digits into sets of 4 starting from the right, padding the leftmost group with zeros if needed, then convert each group directly to its hex digit. For example, 10110110 splits into 1011 and 0110, which are B and 6 in hex, giving 0xB6. This works because 16 is 2 to the 4th power, so each hex digit exactly represents 4 bits with no rounding or remainder. The same grouping trick works for octal using groups of 3 bits, since 8 is 2 cubed.
References
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