This document discusses digital waveforms and timing diagrams. It defines positive and negative pulses as voltage levels that change between high and low states. Key pulse characteristics are described such as rise time, fall time, pulse width, amplitude, leading and trailing edges. Periodic and non-periodic pulses are also defined. Timing diagrams are introduced as a way to synchronize digital waveforms with a clock signal. The clock provides a reference bit time that waveforms can change state on.

1. Number Systems
• Number Systems, Operations and Codes
– Chapter 2 - Self Read
• Read the following sections:
– 2.1 – 2.4
– 2.8
– 2.10
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2. Digital Waveforms
– Consist of voltage levels that change back
and forth between the HIGH and LOW states
– Positive-going pulse – generated when the
voltage goes from LOW level to HIGH level
and back to LOW level
– Negative-going pulse – generated when the
voltage goes from HIGH level to LOW level
and back to HIGH level
– A digital wave from is made-up of a series of
pulses
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3. Digital Waveforms
• Diagram: Positive and negative-going
pulses (page 5)
HIGH
HIGH
Rising or
leading edge
LOW
Falling or
trailing edge
t0
Falling or
leading edge
LOW
t1
Positive-going pulse
Rising or
trailing edge
t0
t1
Negative-going pulse
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4. Digital Waveforms
– Pulse characteristics
• Leading edge (occurs first at t = 0)
• Trailing edge (occurs last at t = 1)
• Positive-going pulse: Leading edge is a rising edge
and trailing edge is falling edge
• Negative-going pulse: Leading edged is falling
edge and trailing edge is rising edge
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5. Digital Waveforms
• Diagram: non-ideal pulse (page 6)
90%
Amplitude
50%
10%
Baseline
Pulse Width, tw
Rise Time, tr
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Fall Time, tf
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6. Digital Waveforms
– Pulse parameters
• Rise time (tr) – is the time required for a pulse to
go from its LOW to HIGH level (measured 10% to
90% of the pulse amplitude)
• Fall time (tf) – is the time required for the transition
from the HIGH to LOW level (measured 90% to
10% of the pulse amplitude)
• Pulse amplitude – height of the pulse from
baseline
• Pulse width (tw) – duration of the pulse (defined
as the time interval between the 50% points on the
rising and falling edges)
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7. Digital Waveforms
– Waveform characteristics
• Most waveforms are composed of a series of
pulses (pulse trains)
• Pulses can be either
– periodic – repeats itself at a fixed interval called a
period (T)).
» The frequency, f, is the rate at which it repeats
itself and is measured in Hertz (H)
– non-periodic – does not repeat itself at fixed
intervals and may be composed of pulses of
different pulse widths.
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8. Digital Waveforms
• Frequency of a pulse, f, is the reciprocal of its
period, T.
– f = 1/T
– T = 1/f
• Duty cycle – the ratio of the pulse width (tw) to the
period (T), expressed as a percentage
– Duty Cycle = (tw/T)x100%
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9. Digital Waveforms - Example
• The following figure shows a periodic digital
waveform. The measurements are in
milliseconds. Determine its period, frequency
and duty cycle.
T
tw
t (ms)
0
1
10
11
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10. Digital Waveforms - Example
• Related exercise:
– A periodic digital signal waveform has a pulse
width of 25 µs and a period of 150 µs.
Determine the frequency and duty cycle.
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11. Timing Diagrams
• Many digital waveforms are synchronized
with a basic timing waveform called the
clock.
• The clock is a periodic waveform in which
each interval between pulses equals one
bit time.
• Example:
• Diagram: Clock waveform: page 8
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12. Timing Diagrams
• Clock waveform
Bit time
Clock
1
0
1
A 0
Bit Sequence
Represented
1
0
1
0
0
1
by waveform A
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13. Timing Diagrams
• Each change in the level of waveform A
occurs at the rising edge of the clock
waveform.
• In other cases, the change occurs at the
trailing edge of the clock.
• During each bit time of the clock,
waveform A is either HIGH or LOW, which
represent a sequence of bits
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14. Timing Diagrams - Exercise
• Given a string of ten alternating 0s and 1s,
show a clock waveform for the string
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15. • End of Lecture
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