IS 151 lecture 2
- 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 1
- 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 2
- 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 IS 151 Digital Circuitry 3
- 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 IS 151 Digital Circuitry 4
- 5. Digital Waveforms • Diagram: non-ideal pulse (page 6) 90% Amplitude 50% 10% Baseline Pulse Width, tw Rise Time, tr IS 151 Digital Circuitry Fall Time, tf 5
- 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) IS 151 Digital Circuitry 6
- 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. IS 151 Digital Circuitry 7
- 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% IS 151 Digital Circuitry 8
- 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 IS 151 Digital Circuitry 9
- 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. IS 151 Digital Circuitry 10
- 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 IS 151 Digital Circuitry 11
- 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 IS 151 Digital Circuitry 12
- 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 IS 151 Digital Circuitry 13
- 14. Timing Diagrams - Exercise • Given a string of ten alternating 0s and 1s, show a clock waveform for the string IS 151 Digital Circuitry 14
- 15. • End of Lecture IS 151 Digital Circuitry 15