Problem #1 Recall that a DNA is composed of 4 different nucleotides, G, C, A, a nucleotides. G. C, A, and T (or U), grouped as 2 C, and A with T). The complementary pairing facilitates transcription of DNA into eotides in sequence are recognized as distinct amino acids. For instance, GGG correspond to glycine. (a) Suppose that we chose a 2-bit binary representation for the nucleo nose a 2-bit binary representation for the nucleotides. We assign G to be holu, nb[0]} = {0,0) = 2'500 (note these different ways we represent this 2-bit nan and is represented as nb1:01=2'b01. What should one choose for C and A TO Tacilitate representing the nucleotides after RNA transcription (which produces a "complement" strand). (0) Special 3 nucleotide sequences are known as a "stop codon" that indicate the end on a gene. They are TAA, TAG, and TGA. The 3 nucleotide sequence when using the encoding in (a) is represented as cb[5:0) where for TAG, bits cb[5:4) are for T, cb[3:2] are for A, and cb[1:0) are for G. Write the logic equation for indicating the detection of a stop codon, S, as a function of cb[5:0) in fully-disjunctive normal form. (c) Apply factoring and other Boolean properties to reduce the result in (b) into an expression using the least number of literals. (d) Instead of binary representation, let us use one-hot representation for the nucleotides, whereby each nucleotide is expressed with 4 bits, coh[3:0) = 4'50001 for G, 4'50010 for C, 4'b0100 for A, and 4'b1000 for T. The codon is represented as a 12-bit combination of 3 nucleotides, coh[11:0). Write a minimal sum-of-products, logic equation for the same indicator for a stop codon, S. (e) Reduce the expression in part (d) and to one using the least number of literals. () One-hot encoding is not difficult to "complement between the nucleotide pairing, G-to-C, C- to-G, A-to-T, and T-to-A. Write the logical equations for cnoh[3:01, the "complemented" nucleotides, from the inputs noh[3:0). Answer the question for all parts in the space below