Digital Design_ Principles and Practices, Chegg Solution Manual_parte_039

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Step 1 of 3 2.035E Consider the following diagram which shows a mechanical encoding disk using a 3-bit binary code. 111 000 001 110 0 0 1 010 101 011 100 Figure 1: Mechanical encoding disk with 3-bit binary code Step 2 of 3 When the contacts made on the disc while rotating, the values in the disc are read according to the connection of the signal source in the disc. The dark areas of the disk gives the value of 1 or logic 1 which is connected to the signal source and light areas in the disc gives the value of 0 or logic 0 which is not connected to the signal source. When the disc is reading at boundaries for example between 101 and 110, two bits are changed between two numbers. When contact is made at boundaries, it reads 1 on the both sides and gives an incorrect reading. These types of boundaries are said to be bad boundaries. This problem can be solved by using gray code. Because only one bit, changes at time. For example when contacts made between the boundaries of 000 and 001, disc will read as 001. Step 3 of 3 When we look in to the diagram, the below list are said to be bad boundaries since two or more of the encoded bits changes. Boundaries Number of encoded bits changed From To 001 010 2 011 100 3 101 110 2 111 000 3 Table 1: List of bad boundaries in mechanical encoded disk with 3 bit. Thus, from the Table 1 the number of bad boundaries are said to be 4 -