Please explain why the poof works. How can we write the DFA using these decimals. How can we write the reverse of B using decimals.

Let 3=000,001.010,111 such that 3 contains all size 3 columns of 0s and 1s. A string of symbols in 3 gives three rows and columns. Consider each row to be a binary number and let B={w3 the bottom row of w is the sum of the top two rows }. Claim: B is regular. Proof: Let the elements of of 3 be denoted by their corresponding decimal value as if reading top to bottom were the same as left to right. (e.g. 001=1 and 110=6 ). The following is a DFA that recognizes BR. 1 Therefore we know that BR is regular, and because regular languages are closed under reverse, B is regular