What is the binary equivalent of the hexadecimal number 2AB16?

Concept

Binary (base 2) and hexadecimal (base 16) are directly related because 16 = 24 — each hexadecimal digit corresponds to a unique group of exactly 4 binary bits. Converting a hexadecimal number to binary means replacing every hex digit with its standard 4-bit binary code and writing the codes in the same left-to-right order, with no digit-to-digit carrying involved.

Application

1. Identify the decimal value of each hexadecimal digit: 2 = 2, A = 10, B = 11.

2. Write the 4-bit binary code for each digit using place values 8-4-2-1: 2 → 0010, A → 1010, B → 1011.

3. Concatenate the three 4-bit codes in the same order as the original digits: 0010 1010 1011.

4. Drop the non-significant leading zero to obtain the final binary value: 1010101011₂.

Cross-check

Reverse the process on the 12-bit string 0010 1010 1011 by splitting it back into 4-bit groups from the right: 0010, 1010, 1011. These map back to the digits 2, A, B, reproducing the original hexadecimal number 2AB16, confirming the conversion is correct.