Asymmetric Numeral Systems (ANS) are an entropy-based encoding method introduced by Jarek Duda, combining the Shannonoptimal compression effectiveness of arithmetic coding with the execution efficiency of Huffman coding. Existing presentations of the ANS encoding and decoding algorithms are somewhat obscured by the lack of suitable presentation techniques; we present here an equational derivation, calculational where it can be, and highlighting the creative leaps where it cannot.