Sequential Circuits
x w
Combinational
v0
Storage
v0+
v1 elements
clock v1+
Huffman Model
A combinational circuit and storage elements are interconnected to form
a sequencial circuit.
The information stored at any time defines the state of the circuit at
that time.
The next state of the storage elements is a function of the inputs and
the present state.
Synchronous sequential circuit can be defined from the knowledge of its
signals at discrete instants.
March 28, 2006 1
Sequential Circuit Design
1- Obtain either the state diagram or state table from the
problem specs.
2- If we don‟t have one already, obtain the state table
from the state diagram.
3- Assign binary codes to the states.
4- Derive the FF input equations from the next state
entries of the state table.
5- Derive the output equations from the output entries of
the state table.
March 28, 2006 2
Sequential Circuit Design
Design a sequence detector for the string “1101”. The
output must be „1‟ when the input matches this string
x Sequence
w
clock detector
March 28, 2006 3
Sequential Circuit Design
Mealy state machine (remember that in this state machine
the output is dependent on input changes and states)
1/0
1/0 1/0 0/0
0/0
A B C D
0/0
1/1
0/0
Assign binary values to each state. Example:
A = 00, B = 01, C = 11, D = 10
March 28, 2006 4
Sequential Circuit Design
Make Table FROM present state & input TO next state &
output, and FF inputs. J K Q(t+1) Operation
0 0 Q(t) No change
0 1 0 Reset
1 0 1 Set
1 1 Q‟(t) Complement
A
B
C
D
March 28, 2006 5
Sequential Circuit Design
K-maps of the states & the outputs
Q1 Q0 Output = IQ1Q0‟
I
00 01 11 10
0 0 0 0 0
1 0 0 0 1
Q1 Q0 J1 = IQ0 Q1 Q0 K1 = Q0‟
I I
00 01 11 10
00 01 11 10
0 0 0 X X 0 X X 0 1
1 0 1 X X 1 X X 0 1
Q1 Q0 J0 = I Q1 Q0 K0 = I‟
I I
00 01 11 10 00 01 11 10
0 0 X X 0 0 X 1 1 X
1 1 X X 1 1 X 0 0 X
March 28, 2006 6
Sequential Circuit Design
Layout Diagram
J1 = IQ0
K1 = Q0‟
J0 = I
K0 = I‟
Output = IQ1Q0‟
March 28, 2006 7
Sequential Circuit Design – Moore State Machine
Associate output with states only. This means that the
output is also synchronous with the clock
x Sequence
w
clock detector
clock
x
w
March 28, 2006 8
Sequential Circuit Design
Moore State Machine for the sequence detector 110
1 1 1 0
0
A/0 B/0 C/0 D/1
0
1
0
clock
x
w
March 28, 2006 state A B C D A 9
Sequential Circuit Design
VHDL implementation for the Moore sequence detector 110
ARCHITECTURE seq_det_arch of seq_det is
BEGIN
ENTITY seq_det IS process1: PROCESS(CLK)
PORT ( VARIABLE STATE : STD_LOGIC_VECTOR(1 DOWNTO 0):= "00";
CLK : IN STD_LOGIC;
BEGIN
X : IN STD_LOGIC; IF (CLK = „1‟) THEN
W : OUT STD_LOGIC CASE STATE IS
); WHEN "00" => -- State A
END seq_det; IF (X = '0') THEN
STATE := "00";
W -- State B
IF (X = '1') THEN
STATE := "10";
W -- State C
IF (X = '1') THEN
STATE := "10";
W -- State D
IF (X = '1') THEN
STATE := "01";
W <= '0';
ELSE
STATE := "00";
W <= '0';
END IF;
END CASE;
END IF;
END PROCESS;
END seq_det_arch;
March 28, 2006 11
Sequential Circuit Design
VHDL implementation for the Moore sequence detector 110
Simulation waveform
March 28, 2006 12