What Is a Number Base Changer?

This is an online browser-based utility for changing a number's base. Numbers are an abstract idea and to write them down, you need to select a base. The base can be anything and the most common base is 10 (decimal) and it's the default base in this tool. When you write a number 25 or 1044, it's assumed that it's in base 10 but it could be in any other base as there are infinitely many numeral systems. Other well-known numeral systems are binary (base 2), octal (base 8), and hexadecimal (base 16). Slightly less common are negative bases, such as negabinary (base -2), negaoctal (base -8), negadecimal (base -10), and negahexadecimal (base -16). Even less common and virtually unknown bases are rational (for example, base 2/3), irrational (for example, base e), fractional (for example, base π/2), imaginary and complex (for example, base i), and many more. At the moment we support only positive and negative integer bases. All bases use the same principle to represent a number with the only difference being the alphabet set of the digits and whether the sign symbol is used for negative numbers. For example, the binary base expresses each number using two characters "0" and "1", the decimal base uses ten digits "0123456789", and the hexadecimal base uses six more letters "0123456789abcdef". Given the alphabet and the base, we can express any number by the formula x = ∑anbn, where an is a digit from the alphabet and b is the given base. The sequence anan-1…a0 of indexes in this formula is the number x in the given base b. For example, in base 10, the number 25 can be written as a sum ∑an10n = a1*101 + a0*100 = 2*101 + 5*100. Here the indexes are a1 = 2 and a0 = 5 and a1a0 forms the number 25. In the base 2, the number 25 can be expressed as 1*24 + 1*23 + 0*22 + 0*21 + 1*20 and from this sum, we find that 11001 is the number 25 in base 2. With negative bases, it works the same way. For example, in base -8, the number 2510 is 1*(-8)2 + 5*(-8)1 + 1*(-8)0, which is 151-8. If the base is negative, then the minus sign is not used. For example, -2510 = 4*(-8)1 + 7*(-8)0 = 47-8. In positive bases, the minus sign needs to be used to express negative numbers. This tool accepts any number with the base from -64 to 64 as input (except bases 0 and -1, which don't exist) and outputs it in any other base from this range. It can convert multiple numbers at the same time if they are entered one per line. As it's not always easy to know what each number means, you can also print the decimal number after each converted number. Also, as sometimes you may need the full sum formula, you can select the "Use Sum Formula" option to print the sum terms. That's numberwang!

What Is a Number Base Changer?

This is an online browser-based utility for changing a number's base. Numbers are an abstract idea and to write them down, you need to select a base. The base can be anything and the most common base is 10 (decimal) and it's the default base in this tool. When you write a number 25 or 1044, it's assumed that it's in base 10 but it could be in any other base as there are infinitely many numeral systems. Other well-known numeral systems are binary (base 2), octal (base 8), and hexadecimal (base 16). Slightly less common are negative bases, such as negabinary (base -2), negaoctal (base -8), negadecimal (base -10), and negahexadecimal (base -16). Even less common and virtually unknown bases are rational (for example, base 2/3), irrational (for example, base e), fractional (for example, base π/2), imaginary and complex (for example, base i), and many more. At the moment we support only positive and negative integer bases. All bases use the same principle to represent a number with the only difference being the alphabet set of the digits and whether the sign symbol is used for negative numbers. For example, the binary base expresses each number using two characters "0" and "1", the decimal base uses ten digits "0123456789", and the hexadecimal base uses six more letters "0123456789abcdef". Given the alphabet and the base, we can express any number by the formula x = ∑anbn, where an is a digit from the alphabet and b is the given base. The sequence anan-1…a0 of indexes in this formula is the number x in the given base b. For example, in base 10, the number 25 can be written as a sum ∑an10n = a1*101 + a0*100 = 2*101 + 5*100. Here the indexes are a1 = 2 and a0 = 5 and a1a0 forms the number 25. In the base 2, the number 25 can be expressed as 1*24 + 1*23 + 0*22 + 0*21 + 1*20 and from this sum, we find that 11001 is the number 25 in base 2. With negative bases, it works the same way. For example, in base -8, the number 2510 is 1*(-8)2 + 5*(-8)1 + 1*(-8)0, which is 151-8. If the base is negative, then the minus sign is not used. For example, -2510 = 4*(-8)1 + 7*(-8)0 = 47-8. In positive bases, the minus sign needs to be used to express negative numbers. This tool accepts any number with the base from -64 to 64 as input (except bases 0 and -1, which don't exist) and outputs it in any other base from this range. It can convert multiple numbers at the same time if they are entered one per line. As it's not always easy to know what each number means, you can also print the decimal number after each converted number. Also, as sometimes you may need the full sum formula, you can select the "Use Sum Formula" option to print the sum terms. That's numberwang!