CS E6831 02s
HWK #10 Solutions
NT-1. 2-input dual-rail XOR-gate
Z1 = A1B0 + A0B1 Z0 = A1B1 + A0B0
NT-2. Modify the design of the asynchronous counter to make it
recycle to state 000 after state 100.
Continuing my efforts to avoid diagrams in the solutions, I will simply
give logic expressions for each TFF input, and for output A. I am
labeling the TFF's from left to right (let significant bit) 2, 1, and
0.
Then T0 = RQ2' (To keep the first FF form going on when the state is
100.)
T1 = T0Q0 (as in the basic counter, i.e., T1 = RQ2'Q0
T2 = T1Q1 + RQ2 (make Q2 go off when the state is 100.)
NT-3. Generate a reduced flow table for an action doubler.
The primitive flow table is shown below. Note that O" means consider
this symbol as a 0 if the row is NOT merged with another row, but,
for purposes of flow table reduction treat it as a don't care.
Similarly for 1". The total states marked with * are the possible
starting states, i.e., states where a change in Ss is expected, to
initiate action.
SsFp
00 01 11 10
1 (1),00* 2,0"0
2 3,1"0 (2),10
3 (3),00 4,00"
4 5,0"1 (4),01"*
5 (5),11 6,1"1
6 1,01" (6),01
SpFs
By merging 126 and 345, the table is easily reduced to that shown
below.
SsFp
00 01 11 10
(126) 1 (1),00 (1),01 2,00 (1),10
(345) 2 (2),11 1,11 (2),00 (2),01
SpFs
NT-4. Show how to use the action doubler as a component to produce an
action quadrupler, or, in general, a system for producing 2^n actions
from a single start-signal.
Use two doublers, the Sp output of the first feeding the Ss input of
the second, and the Fs signal from the second feeding back to the Fp
input of the first. A chain of k doublers produces 2^k actions.
NT-5. Show how to convert the flow table for the IF-box to one for a
while-box.
At the point where, in the IF-process, the process controlled has
turned off the Ap-signal, the next step in the IF-process is to turn
on the As signal, to indicate to the environment that the sequence is
now complete. Prior to this last point, the sequence is identical to
what we would want for a while box. For the while box, instead of
terminating the process, the controller should return to the state
where the value of X is interrogated. So, instead of turning on As,
the controller should go to the total state reached when Rs was first
turned on. In this state, Rx is turned on.
A primitive flow table for the WHILE box is shown below. For the
IF-box, we would change the entry 2,000" in state 4-1000 to 4,000".
(The original problem statement was erroneous in stating that "the
change also eliminates a row of the primitive table".)
RsX1X0Ap
0000 1000 1010 1100 1001
1 (1),000 2,0"00
2 (2),100 3,1"00 5,1"00
3 4,000" (3),000
4 1,001" (4),001
5 6,000 (5),000
6 (6),010 7,01"0
7 2,0"00 (7),000
RxRpAs
.............
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