Base Converter CalculatorFree online math calculator — instant results, no sign-up

N = s × Σ(i = 0 to k − 1) d_i b^i = s × Σ(j = 0 to m − 1) e_j c^j. For the default inputs: N = 1×2^5 + 0×2^4 + 1×2^3 + 1×2^2 + 0×2^1 + 1×2^0 = 45. Since 45 = 2×16 + 13 and digit value 13 is D, 101101 in base 2 = 2D in base 16.

• NThe integer value, which remains unchanged during conversion.
• sThe sign multiplier: +1 for a nonnegative integer and −1 for a negative integer.
• bThe source base; 2 in the worked example.
• cThe target base; 16 in the worked example.
• d_iThe numeric value of the source digit at position i, counting from the right starting at zero.
• e_jThe numeric value of the target digit at position j, counting from the right starting at zero.
• k, mThe number of source digits and target digits, respectively, excluding the sign.
• i, jThe source and target position indices used in the positional-value sums.

Separate the sign from the digits and check that both bases are integers from 2 through 36. Map digits 0–9 to values 0–9 and letters A–Z to values 10–35, rejecting any digit whose value is at least the source base. Evaluate the input magnitude using source-base place values, then repeatedly divide it by the target base, collecting remainders. Read the remainders in reverse order, encode values above 9 as letters, and restore the negative sign if needed. Represent zero as 0.

These are the calculator's starting values and the results it actually produces for them.

1. 1Enter 101101 in Integer for the default worked example.
2. 2Set Source base to 2 so the input is read as binary.
3. 3Set Target base to 16 to request hexadecimal output.
4. 4Run the conversion; the binary place values sum to 45, and division by 16 gives quotient 2 and remainder 13.
5. 5Read Converted integer as 2D, where D represents the remainder value 13.