IS 151 Digital Circuitry 1

Number Systems

• Number Systems, Operations and Codes – Chapter 2 - Self Read

• Read the following sections:– 2.1 – 2.4– 2.8– 2.10

IS 151 Digital Circuitry 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

IS 151 Digital Circuitry 3

Digital Waveforms

• Diagram: Positive and negative-going pulses (page 5)

t0 t1

HIGH

LOW LOW

HIGH

Rising or leading edge

Falling or trailing edge

Falling or leading edge

Rising or trailing edge

Positive-going pulse Negative-going pulse

t0 t1

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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

IS 151 Digital Circuitry 5

Digital Waveforms

• Diagram: non-ideal pulse (page 6)

Amplitude

BaselinePulse Width, tw

Rise Time, tr Fall Time, tf

90%

50%

10%

IS 151 Digital Circuitry 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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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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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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Digital Waveforms - Example

• The following figure shows a periodic digital waveform. The measurements are in milliseconds. Determine its period, frequency and duty cycle.

0 1 10 11t (ms)

Ttw

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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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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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Timing Diagrams

• Clock waveform

Clock

Bit time

1

0

1

A 0

Bit Sequence

Represented 1 0 1 0 0 1

by waveform A

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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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Timing Diagrams - Exercise

• Given a string of ten alternating 0s and 1s, show a clock waveform for the string

IS 151 Digital Circuitry 15

• End of Lecture