Convert the hexadecimal number 1B0 into its binary equivalent.

Concept

Each hexadecimal digit maps to exactly 4 binary bits (because 16 = 24). To convert a hex number to binary, replace every hex digit independently with its fixed 4-bit pattern and concatenate the groups in the same order. The base-16 to base-2 relationship makes this a direct one-digit-to-four-bits substitution, with no carrying or arithmetic across digits.

Application

The number 1B0 has three hex digits, so the binary result has 3 × 4 = 12 bits. Substitute each digit with its 4-bit group:

Concatenate the groups left to right in the original order:

1. Digit 1 → 0001

2. Digit B → 1011

3. Digit 0 → 0000

4. Join: 0001 1011 0000 → 000110110000

So 1B0₁₆ = 000110110000₂.

Cross-check

Read the binary value back: 000110110000 groups into 0001 1011 0000 = 1, 11, 0 = 1, B, 0 = 1B0. As an independent check, 1B0₁₆ = 1×256 + 11×16 + 0 = 256 + 176 + 0 = 432, and 000110110000₂ = 256 + 128 + 32 + 16 = 432. Both confirm the result.