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Digital Logic Design

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CS302 - Digital Logic & Design
Lesson No. 26
THE 555 TIMER
The 555 Timer is a versatile and widely used device which can be configured as a
mono-stable One-Shot or as an Astable multivibrator. An Astable multivibrator is known as an
Oscillator which does not have any stable state. Therefore it continuously changes from one
unstable state to the other without any external trigger.
Timing Problem in flip-flop circuits
In synchronous digital circuits the output of one flip-flop is connected to the input of a
second flip-flop, either directly or through logic gates. Both the flip-flops are triggered through a
common clock signal connected to the clock input of both the flip-flops. This leads to a
potential timing problem as shown in figure 26.1.
Figure 26.1a
J-K flip-flop circuit with potential timing problem
Figure 26.1b
Timing diagram of J-K flip-flop circuit with potential timing problem
Assume the initial outputs of flip-flop 1 and 2 are at logic high and low respectively.
When there is a high to low clock transition t1, the output of flip-flop 1 toggles to logic low. The
high to low clock transition at the clock input of Flip-flop 2 also occurs at the same instant t1.
During the interval t1 and t2 the output of flip-flop is changing from logic high to logic low and
will go to logic low after a propagation delay tPHL. The input to flip-flop 2 is changing from logic
high to low during the time interval t1 and t2. The input to flip-flop 2 should be held stable for a
minimum hold time requirement tH. If the input is not held stable for tH interval the output can
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not be guaranteed to be logic high. Output of flip-flop 2 will be set to logic high state if tPHL time
of flip-flop 1 is more than the tH of flip-flop 2. Practically flip-flops have hold times that are 5
nsec or less, most have tH = 0. Therefore, flip-flop circuits such as the one shown connected in
the diagram work reliably.
Clock Skew
One of the most common problems in synchronous circuits is `Clock Skew'. One type
of Clock Skew occurs when the same clock signal arrives at different times at different clock
inputs to propagation delay, which causes different flip-flops to change states asynchronously
leading to unpredictable outputs. Figure 26.2
Figure 26.2a Flip-flop circuit with potential timing problem due to Clock Skew
Figure 26.2b
Timing diagram of J-K flip-flop circuit with Clock Skew
In the circuit diagram both the flip-flops are connected to the same clock signal.
However, the clock signal to the second flip-flop is delayed by the NAND and NOT gates. On a
high to low clock transition both the flip-flops change their output states assuming that the
initial output state of each flip-flop is logic low. The Clock Skew is the delay in the two clock
signals by a time interval t1 t2 or t3 t4. At the high to low transition of clock 1 signal the output of
F1 toggles from logic low to logic high after a propagation delay of tPLH. If the propagation
delay of F1 is less than the clock skew then at the high to low clock transition of clock 2 the J
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input of flip-flop is set to logic high and at the clock transition the output F2 is set to logic high.
If the propagation delay tPLH of F1 is of a longer duration than the Clock Skew, the J input of
the flip-flop is at logic low at the high to low transition of clock 2 the output of F2 remains
unchanged.
Timing problems occurring due to clock skew are intermittent in nature and therefore
are difficult to detect. The clock skew can vary with changes in temperature, power supply
voltages, length of connections and loading effects. Problems caused due to clock skew can
be eliminated by equalizing clock delays to different parts of the circuit.
Race Conditions
Race conditions are said to occur when multiple internal variables change due to
change in one input variable. Depending upon the sequence in which the internal variables
change, the circuit output operates erratically. Figure 26.3. In the timing diagram shown, if the
Q and Q output high to low transitions are slightly delayed, they coincide with the clock low to
high transitions resulting in short duration pulses which are difficult to detect. The glitches due
to race condition can be avoided by using a negative-edge triggered flip-flop instead of the
positive-edge-triggered flip-flop used.
Figure 26.3a
J-K flip-flop circuit with potential race condition
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CS302 - Digital Logic & Design
Q
Figure 26.3b
Timing Diagram showing glitches due to race conditions
Q
Figure 26.3c
Timing Diagram of negative-edge triggered flip-flop avoiding glitches
Counters
Counter circuits based on flip-flops are widely used in Digital Systems. Besides
counting, these counters are used as frequency dividers and with minor changes in the circuit
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they are used as shift registers. Counters are classified as Asynchronous and Synchronous
counters. Asynchronous counters as the name indicates are not triggered simultaneously. The
multiple flip-flops that are connected together to form a counter circuit do not receive the
triggering clock signal simultaneously. The flip-flop that represents the least significant count
bit of the n-bit counter is connected to the clock signal, the remaining flip-flops receive their
clock signals form the outputs of the preceding flip-flops connected in the counter circuit. The
clock signal thus ripples through successive flip-flops. Synchronous counters on the other
hand have all the clock inputs of the multiple flip-flops connected to a common clock signal. All
the flip-flops in a Synchronous counter receive clock signals simultaneously.
Asynchronous and Synchronous are further classified as up counters or down counters
depending upon the sequence in which they count. They are further classified in terms of the
number of states or the range of numbers to which the counters can count.
Asynchronous Counters (Ripple Counters)
Asynchronous counters are implemented by connecting together multiple flip-flops
together. The triggering clock signal is connected to the clock input of the first flip-flop. The
clock inputs of the remaining flip-flops are connected to the Q or Q output of the previous flip-
flop. On a clock transition at the clock input of the first flip-flop the output state of the flip-flop
changes. With the transition in the output state of the first flip-flop, there is also a transition at
the clock input to the second flip-flop as the output of the first flip-flop is connected to the clock
input of the second flip-flop. Due to the clock transition the second flip-flop changes its output
state. The change in the output state of the second flip-flop occurs after the first flip-flop
changes its state. Similarly, the last flip-flop connected in the counter circuit changes its output
state after the output of the flip-flop connected to its clock input has changed it state. The
outputs of the flip-flops change in a sequence as the clock signal propagates through the flip-
flops as they change their output states one after the other. The Asynchronous counters are
also known as Ripple Counters due to the rippling effect of the clock signal.
A three-bit Asynchronous counter circuit is shown in Figure 26.4. In the circuit diagram
shown the Q output of each is connected to the clock input of the next flip-flop. The J-K inputs
of each of the three flip-flop are connected to logic high allowing the flip-flop to toggle their
output state on a high to low transition at their clock input.
The output state of the first flip-flop toggles at every positive to negative clock transition
in intervals t1 to t8. The output F1 of the second flip-flop toggles at intervals t2, t4, t6 and t8 on
every high to low transition of the output F0. The output F2 toggles its output state at intervals t4
and t8 on a high to low transition of the flip-flop output F1.
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Figure 26.4a 3-bit Asynchronous Up-Counter
CLOCK
Input
F0
Output
F1
Output
F2
Output
t1
t2
t3
t4
t5
t6
t7
t8
Figure 26.4b Timing Diagram of a 3-bit Asynchronous Up-Counter
Input
Output
Clock
F2
F1
F0
Pulses
1
0
0
0
2
0
0
1
3
0
1
0
4
0
1
1
5
1
0
0
6
1
0
1
7
1
1
0
8
1
1
1
Table 26.1
Output State of a 3-bit Asynchronous Up-Counter
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Propagation Delay
The timing diagram shown in figure 26.4b doesn't take into account the propagation
delay that occurs between each clock input and the corresponding toggling output. The timing
diagram which takes into account the propagation delay is shown in figure 26.5. At time
interval t4 on a clock transition the output F0 toggles to a new state after a delay determined by
tPHL propagation delay of the first flip-flop. At interval t5 on the high to low transition of the F0
output, the output F1 toggles to a new state after a propagation delay tPHL of the second flip-
flop. Finally, at interval t6 the transition in F1 output toggles the output F2 of the third flip-flop.
The output F2 becomes stable after a propagation delay tPLH of the third flip-flop. The
propagation delay of each of the three flip-flop adds up to delay the output F2 by three
propagation delays with respect to the clock transition at interval t4. If the counter circuit is
extended by adding more flip-flops, then the output of the last flip-flop might exceed the clock
period of the clock which causes timing problems. The Asynchronous counters can not work at
high clock frequencies and cause problems with decoding circuits.
CLOCK
Input
F0
Output
F1
Output
F2
Output
t4 t5 t6 t7
t1
t2
t3
Figure 26.5
Timing Diagram of a 3-bit Asynchronous with propagation delay
The timing diagram of the 3-bit counter circuit using a clock of a higher frequency is
shown in Figure 26.6a. At interval t4, the negative clock transition toggles the F0 output to logic
low at interval tA after a propagation delay of tPHL. The negative transition of F0 at tA toggles the
F1 output to logic low at interval t5 after a propagation delay of tPHL. Finally, the F2 output is
toggled to logic high at interval tB after a delay of tPLH after the clock (F1) transition at interval t5.
The output states of the counter at intervals t1 to t7 are shown in table 26.2. The output at
interval t5 should be 100 instead of 010.
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Figure 26.6a Timing Diagram of a 3-bit Asynchronous with high frequency clock
Input
Output
Clock
F2
F1
F0
Pulses
1
0
0
0
2
0
0
1
3
0
1
0
4
0
1
1
5
0
1
0
6
1
0
1
7
1
1
0
Table 26.2
Output of a 3-bit Asynchronous Up-Counter with high frequency clock
Mod-n Counters
The term Mod represents the Modulus of the counter which is the total number of
unique states through which the counter will sequence through. A 3-bit Asynchronous counter
can count up from 0 to 7 or count down from 7 to 0. The 3-bit counter has 8 different states
represented by the 8 outputs 0 to 7. The counter states or the range of numbers of a counter is
determined by the formula 2m. where m represents the number of flip-flops. Therefore, a Mod-
8 counter implemented using three flip-flops 23 has 8 output states.
Counter can also be designed to have less number of states than 2m. The resulting
sequence is called a truncated sequence. The counter therefore counts up to the truncated
sequence. Designing a truncated sequence counter is very simple. When the counter counts
up to the intended sequence it is reset to the initial count value 0. The counter is reset to the
initial count value by activating the Clear asynchronous inputs. The clears input is activated by
the counter through a combinational circuit that activates its output when the appropriate count
sequence is reached. The Mod-6 counter is shown in figure 26.7.
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F0
F1
F2
J-K flip-flop 1
J-K flip-flop 2
J-K flip-flop 3
1
1
1
SET
SET
SET
Q
Q
Q
CLK
Q
Q
Q
CLR
CLR
CLR
Figure 26.7a Mod-6 Counter
Figure 26.7b Timing diagram of a Mod-6 Counter
The counter counts from state 000 to 101. At interval t6 the counter counts to 110. The
outputs F1 and F2 of the counter are connected to the inputs of a 2-input NAND gate, which
sets its output to logic zero when both its inputs become logic 1 at interval t6. The output of the
NAND gate is connected to the three active-low asynchronous Clear input of the three flip-
flops which are set to low by the NAND gate. Therefore the counter is immediately reset to
state 000 from where it proceeds to sequence through the count values. The Mod number of
the counter also determines the frequency at the output of the counter. The output at F2 has a
frequency which is 1/6th of the input clock frequency. Thus Mod-n counters can be design to
generate 1/nth frequency signal with respect to the input clock signal.
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Mod-10 Counter (Decade Counter)
A decade counter uses four-flip-flops to implement the circuit which counts up to 10
unique states (0000 to 1001). The counter is reset when it counts to the next state 1010. The
frequency of the output signal is 1/10th the input clock frequency. Figure 26.8.
F0
F1
F2
F3
J-K flip-flop 1
J-K flip-flop 2
J-K flip-flop 3
J-K flip-flop 4
1
1
1
1
SET
SET
SET
SET
Q
J
Q
J
Q
J
Q
J
CLK
Q
K
Q
K
Q
K
Q
K
CLR
CLR
CLR
CLR
Figure 26.8a
Asynchronous Decade Counter
Figure 26.8b Timing diagram of a Decode Counter
The output F1 and F3 are connected through a NAND gate to the active-low clear inputs
of all the four flip-flops. The counter counts from 0000 to 1001 (ten output states), when it
counts to 1010, the output of the NAND gate is set to logic low which resets all the four flip-
flops to state 0000.
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Integrated Circuit Asynchronous Counters
Asynchronous Counters are available in Integrated Circuit form. The 74LS93A is a 4-bit
Asynchronous Counter. The counter has two separate clock inputs CLK A and CLK B
connected to the clock input of the first and second flip-flop respectively. The second, third and
fourth flip-flops are internally connected as a ripple 3-bit counter. The counter also has two
inputs pins connected to the inputs of a 2-input NAND (internal) gate, the output off which is
connected to the clear inputs of all the four flip-flops. The counter provides four outputs, one
form each flip-flop. Figure 26.9
CLK B
SET
SET
SET
SET
Q
J
Q
J
Q
J
Q
J
flip-flop 1
flip-flop 2
flip-flop 3
flip-flop 4
CLK A
Q
K
Q
K
Q
K
Q
K
CLR
CLR
CLR
CLR
RO 1
RO 2
Q0
Q1
Q2
Q3
Figure 26.9
Internal circuit diagram of the 74LS93A Counter
The 74LS93A can be configured as MOD-16 counter by connecting CLK B input pin to
the Q0 output pin of the IC. RO 1 and RO 2 are connected to logic low. A Decade counter can
be implemented by connecting CLK B input to the Q0 and Q1 and Q3 outputs to RO 1 and RO
2 respectively. Figure 26.10 Two 74LS 93As ca be cascaded together to form a larger counter.
A MOD-50 counter is implemented using two 74LS93A ICs. Figure 26.11
Figure 26.10a 74LS93A connected as MOD-16 Counter
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CLKA
74LS93A
CLKB
Q0 Q1 Q2 Q3
Figure 26.10b 74LS93A connected as Decade Counter
Figure 26.11 74LS93A Connected as a frequency divider (divide by 50)
In the circuit diagram two 74LS93As are connected together to form a frequency
divider which divides the input frequency by 50. The first 74LS93A is connected to divide the
input frequency by 10. The Q3 output of the first 74LS93A is connected to the CLKB input of
the second 74LS93A. The second 74LS93A is connected to divide the input frequency at
CLKB by 5. The Q3 output of the second 74LS93A therefore provides an output which is 1/50th
of the clock applied at the CLKA input of the first 74LS93A. The second 74LS93A requires the
use of only three flip-flops, therefore the first flip-flop with clock input CLKA is left unconnected.
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Table of Contents:
  1. AN OVERVIEW & NUMBER SYSTEMS
  2. Binary to Decimal to Binary conversion, Binary Arithmetic, 1’s & 2’s complement
  3. Range of Numbers and Overflow, Floating-Point, Hexadecimal Numbers
  4. Octal Numbers, Octal to Binary Decimal to Octal Conversion
  5. LOGIC GATES: AND Gate, OR Gate, NOT Gate, NAND Gate
  6. AND OR NAND XOR XNOR Gate Implementation and Applications
  7. DC Supply Voltage, TTL Logic Levels, Noise Margin, Power Dissipation
  8. Boolean Addition, Multiplication, Commutative Law, Associative Law, Distributive Law, Demorgan’s Theorems
  9. Simplification of Boolean Expression, Standard POS form, Minterms and Maxterms
  10. KARNAUGH MAP, Mapping a non-standard SOP Expression
  11. Converting between POS and SOP using the K-map
  12. COMPARATOR: Quine-McCluskey Simplification Method
  13. ODD-PRIME NUMBER DETECTOR, Combinational Circuit Implementation
  14. IMPLEMENTATION OF AN ODD-PARITY GENERATOR CIRCUIT
  15. BCD ADDER: 2-digit BCD Adder, A 4-bit Adder Subtracter Unit
  16. 16-BIT ALU, MSI 4-bit Comparator, Decoders
  17. BCD to 7-Segment Decoder, Decimal-to-BCD Encoder
  18. 2-INPUT 4-BIT MULTIPLEXER, 8, 16-Input Multiplexer, Logic Function Generator
  19. Applications of Demultiplexer, PROM, PLA, PAL, GAL
  20. OLMC Combinational Mode, Tri-State Buffers, The GAL16V8, Introduction to ABEL
  21. OLMC for GAL16V8, Tri-state Buffer and OLMC output pin
  22. Implementation of Quad MUX, Latches and Flip-Flops
  23. APPLICATION OF S-R LATCH, Edge-Triggered D Flip-Flop, J-K Flip-flop
  24. Data Storage using D-flip-flop, Synchronizing Asynchronous inputs using D flip-flop
  25. Dual Positive-Edge triggered D flip-flop, J-K flip-flop, Master-Slave Flip-Flops
  26. THE 555 TIMER: Race Conditions, Asynchronous, Ripple Counters
  27. Down Counter with truncated sequence, 4-bit Synchronous Decade Counter
  28. Mod-n Synchronous Counter, Cascading Counters, Up-Down Counter
  29. Integrated Circuit Up Down Decade Counter Design and Applications
  30. DIGITAL CLOCK: Clocked Synchronous State Machines
  31. NEXT-STATE TABLE: Flip-flop Transition Table, Karnaugh Maps
  32. D FLIP-FLOP BASED IMPLEMENTATION
  33. Moore Machine State Diagram, Mealy Machine State Diagram, Karnaugh Maps
  34. SHIFT REGISTERS: Serial In/Shift Left,Right/Serial Out Operation
  35. APPLICATIONS OF SHIFT REGISTERS: Serial-to-Parallel Converter
  36. Elevator Control System: Elevator State Diagram, State Table, Input and Output Signals, Input Latches
  37. Traffic Signal Control System: Switching of Traffic Lights, Inputs and Outputs, State Machine
  38. Traffic Signal Control System: EQUATION DEFINITION
  39. Memory Organization, Capacity, Density, Signals and Basic Operations, Read, Write, Address, data Signals
  40. Memory Read, Write Cycle, Synchronous Burst SRAM, Dynamic RAM
  41. Burst, Distributed Refresh, Types of DRAMs, ROM Read-Only Memory, Mask ROM
  42. First In-First Out (FIFO) Memory
  43. LAST IN-FIRST OUT (LIFO) MEMORY
  44. THE LOGIC BLOCK: Analogue to Digital Conversion, Logic Element, Look-Up Table
  45. SUCCESSIVE –APPROXIMATION ANALOGUE TO DIGITAL CONVERTER