2. Write down a valid sum-of-products Boolean expression for each of the outputs. Then, using the laws of Boolean algebra, simplify the expressions. (Please review the truth table in Question 1 before answering question 2)

Question 4: Gray Code Incrementer (40 marks) A Gray code is an alternate binary integer representation with the special property that the encodings of successive numbers differ only by a single binary digit (bit). They have applications in engineering, mathematics and computer science. An en- coding of the first 16 unsigned integers using a Gray code is given here: Decimal Gray 0000 0001 0011 0010 0110 0111 0101 0100 1100 1101 1111 1110 1010 1011 1001 1000 EBoo voor A CONO 15 Note that we can wrap around from 15 back to 0 by also changing only a single bit. In this question you will design a Gray code incrementer, which is a circuit which accepts a 4-bit Gray code Az A, A1 A, as input and outputs the Gray code B2B2B,B For the next number (rolling over to the representation of (0)10 if the input represents (15)10 - 1. Construct the truth table for this circuit showing the outputs (the B;'s) as functions of the inputs. (10 marks) . . . . . . . . o o o o o o o 1 o o o o o o oo To oo 11 o To 1 o Too II) o | | | | 0 0 0 | o o o o o ! 1 ! To To To 11 To TT1 o o II o o | To | 0 000 Question 4: Gray Code Incrementer (40 marks) A Gray code is an alternate binary integer representation with the special property that the encodings of successive numbers differ only by a single binary digit (bit). They have applications in engineering, mathematics and computer science. An en- coding of the first 16 unsigned integers using a Gray code is given here: Decimal Gray 0000 0001 0011 0010 0110 0111 0101 0100 1100 1101 1111 1110 1010 1011 1001 1000 EBoo voor A CONO 15 Note that we can wrap around from 15 back to 0 by also changing only a single bit. In this question you will design a Gray code incrementer, which is a circuit which accepts a 4-bit Gray code Az A, A1 A, as input and outputs the Gray code B2B2B,B For the next number (rolling over to the representation of (0)10 if the input represents (15)10 - 1. Construct the truth table for this circuit showing the outputs (the B;'s) as functions of the inputs. (10 marks) . . . . . . . . o o o o o o o 1 o o o o o o oo To oo 11 o To 1 o Too II) o | | | | 0 0 0 | o o o o o ! 1 ! To To To 11 To TT1 o o II o o | To | 0 000