Page 19, Exercise 1.9 (10 marks)

Figure 1.7 c

Exercise 1.9 Gray Codes. A continuous value that has been quantized into N states can be encoded into an n = ceiling(log₂N) bit signal in which adjacent states differ at most one bit position. Show how the eight temperatures of Figure 1.7 c can be encoded into three bits in this manner. Make your encoding such that the encodings of 82F and 68F also differ in just one bit position.

Continuous Quantities 000 68 001 70 010 72 011 74 100 76 101 78 110 80 111 82 0001111 0000000 68 000000170 000001172 0000111 76 78 80 82 74 Figure 1.7 c