Binary Number System Converter

A number system assigns values to written digits according to a base, also called a radix. Decimal uses base 10 and the digits zero through nine. Binary uses base 2 and only zero and one. Octal uses base 8 and digits zero through seven. Hexadecimal uses base 16, extending the decimal digits with A through F for values ten through fifteen. The same quantity can be represented in every system even though its written form changes. Computers store information as binary states, making base 2 fundamental to digital electronics and programming. Binary strings can become long, so octal and hexadecimal provide compact groupings. Each hexadecimal digit corresponds exactly to four binary bits, while each octal digit corresponds to three bits. For example, decimal 255 is binary 11111111, hexadecimal FF, and octal 377. These are four notations for one integer, not four different values. This converter lets any of the four fields act as the source. Entering a value clears the other fields and records the number system you are using. When you select Convert Number, the tool validates the allowed digits, parses the source value, and writes the equivalent decimal, binary, hexadecimal, and octal strings. Hexadecimal output uses uppercase letters for readability. Leading zeros are omitted because they do not change the numeric value. Place value explains the conversion process. In binary, positions from right to left represent powers of two: one, two, four, eight, and so on. The binary number 101010 therefore equals 32 plus 8 plus 2, or decimal 42. In hexadecimal, 2A equals two groups of sixteen plus ten, which is also 42. In octal, 52 equals five groups of eight plus two, again producing 42. The calculator accepts nonnegative integers that fit safely within JavaScript's exact integer range. It intentionally avoids fractions and signed two's-complement interpretation because those require choices about precision, word length, and encoding. A binary string beginning with one is treated as a positive magnitude, not automatically as a negative signed value. For bit-level programming tasks, establish the intended word size before interpreting a pattern as signed. Use this converter when checking programming constants, learning place value, translating digital logic values, reading permissions, or comparing encoded identifiers. For manual verification, group binary digits from the right in sets of four for hexadecimal or sets of three for octal. Keeping the source base explicit prevents errors such as treating decimal 1010 as binary 1010, which represents decimal ten.