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Unformatted text preview: " 4~1. Design a combinational circuit that forms the 2bit binary sum 5150 of two
2bit numbers A1A0 and B130 and has both a carry input C0 and carry
output C2. Design the entire circuit implementing each of the three outputs
with a twolevel circuit plus inverters for the input variables. Begin the
design with the following equations for each of the two bits of the adder: St. = Xi‘g‘ici +EBiEj. +AiB—ia +AiBiCi 54. C lock and D waveforms, one latch, and two ﬂipflops are shown in Figure 537.
For the latch and each of the ﬂip—ﬂops, carefully sketch the output
waveform, Qi, obtained in response to the input waveforms. Assume that the
propagation delay of the storage elements is negligible. lnitially, all storage
elements store 0. 5~6. A sequential circuit with two D flip—ﬂops A and B, two inputs X and Y, and
one output Z is speciﬁed by the following input equations: DA 2 36A +XY, DB = 333 +XA, Z 2 X8 (3) Draw the logic diagram of the circuit.
(b) Derive the state table.
(c) Derive the state diagram. Blimp Q1 l l C o D with 1 Control '
D s Ll t l c—i T “ f1 Triggered D 03"leth J‘ Triggered D
E] FIGURE 537 Waveforms and Storage Element for Problem 54 D C t 5—8. A sequential Circuit has one ﬂip—ﬂop Q, two inputs X and Y, and one output
S. The Circuit consists of a D ﬂipflop with S as its output and logic
implementing the function D:X®Y€BS with D as the input to the D ﬂip—ﬂop. Derive the state table and state
diagram of the sequential Circuit. 5—9. Starting from state 00 in the state diagram of Figure 5—17(a), determine the
state transitions and output sequence that will be generated when an input
sequence of 10011011110 is applied. 5—10. Draw the state diagram of the sequential circuit speciﬁed by the state table
in Table 5—15‘ El TABLE 515
State Table for Circuit of Problem 510 Present State Inputs Next State Output
A B X Y A B 2
“WW
0 0 0 0 0 0 0
0 0 O 1 0 1 0
0 0 1 0 1 0 1
0 0 1 1 1 1 1
0 1 0 0 0 1 ‘1
0 1 0 1 1 t) 1
O 1 1 0 1 O 0
0 1 l 1 0 0 0
l, 0 0 0 1 l 1
1 0 t) l 1 ‘1 0
1 0 1 0 1 1 1
1 O 1 1 1 0 0
1 1 0 0 0 O 0
1, 1 0 1 0 0 1
1 1 1 O 0 O 0
1 1 1 1. O 1 1 ...
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 Fall '07
 WOLF

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