(Solved) : Question 4 Gray Code Incrementer 40 Marks Gray Code Alternate Binary Integer Representatio Q44101393 . . .
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 3 0010 4 0110 0111 0101 6. 0100 1100 1101 10 1111 1110 11 12 1010 13 1011 1001 14 15 1000 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 A3A2A1 Ao as input and outputs the Gray code B3B2B¡Bo 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) 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. (15 marks) 3. Draw the circuit diagram for your 4-bit Gray code incrementer in logisim- evolution. Try to use as few gates as possible. Be sure to test your circuit by verifying its behaviour in logism-evolution. (15 marks) Show transcribed image text 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 3 0010 4 0110 0111 0101 6. 0100 1100 1101 10 1111 1110 11 12 1010 13 1011 1001 14 15 1000 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 A3A2A1 Ao as input and outputs the Gray code B3B2B¡Bo 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) 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. (15 marks) 3. Draw the circuit diagram for your 4-bit Gray code incrementer in logisim- evolution. Try to use as few gates as possible. Be sure to test your circuit by verifying its behaviour in logism-evolution. (15 marks)
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Answer to Question 4: Gray Code Incrementer (40 marks) A Gray code is an alternate binary integer representation with the special …
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