Quater-imaginary base

The quater-imaginary base, often denoted as \( q = \frac{1}{2} + \frac{1}{2}i \), is a complex numeral system based on the imaginary unit \( i \) and the concept of quaternions. However, the quater-imaginary base specifically refers to a base-2 complex number system that uses the imaginary unit as part of its base.