Exercises 6 (7 pts)

 1. (2 pts) Implement a code convertor for four-bit binary to four-bit Gray code using:
a.    16 entry memory table.
b.    A four bit binary decoder (see Figure 9.1, page 242) and a four bit Gray code encoder. See Figure 9.12, page 252 for binary encoder definition, assume the Gray code encoder operates identically but outputs the appropriate Gray code on yn-1-y0.
2. (2 pts) To implement a 256-input multiplexer:
a.    How many 4-input multiplexers are needed?
b.    How many levels will there be?
3. (2 pts) Implement the function f(a,b,c,d)=one-set(1,3,4,9,14,15) using an eight-input multiplexer (see Section 9.4.1).
a.    Simplify the corresponding K-map at left to an expression of three variables a, b, and c.
 
      f   cd
       \00 01 11 10 
  ab 00|0 |1 |1 |0 |
     01|1 |0 |0 |0 |
     11|0 |0 |1 |1 |
     10|0 |1 |0 |0 |		      f   c
      \0   1 
 ab 00| d|  |
    01|  |  |
    11|  |  |
    10|  |  |

The a=0, b=0, c=0 entry is d has been done as an example. It can be seen in the table below to be d  because for cd = 00 the output f =0 and for cd = 01, the output f =1, hence f=d.

      f   cd
       \00 01
  ab 00| 0| 1
b.    Give the eight inputs (x0-x7) to the resulting 8-input multiplexer solution. Recall that when abc = 000, x0 is selected, when abc=001, x1 is selected, etc.
4. (1 pt) Give an example to show that the network in Figure 9.39 on page 275 of the text can be used to connect xi to yi. This network is used for bit-serial communications. It is sifficient to describe one case, say x3 and y3, to show that xi = yi.