Date of Award

Winter 3-7-2023

Document Type

Thesis (Undergraduate)


Computer Science

First Advisor

Thomas H. Cormen


A Gray code is a sequence of n binary integers in the range 0 to n-1 that has the Gray-code property: each integer in the sequence differs from the integer before it in a single digit. Gray codes have many applications, ranging from rotary encoders to Boolean circuit minimization. We refer to Gray codes where the first and last
codewords in the sequence fulfill the Gray-code property as cyclic. Additionally, we refer to a Gray code as dense if the sequence of n numbers consists of a permutation of ⟨0, 1, . . . , n − 1⟩. This thesis focuses on generating mixed-radix Gray codes under a variety of starting conditions. Mixed radix is a base representation that uses any d-tuple of radices r = (r_d−1, r_d−2, . . . , r_0) where each digit position can have a different base. This thesis will address a method to create a dense, cyclic Gray code for mixed radices when r_d−1 = 2, there is at least one odd radix, and n is odd.