# Digital Electronics

**Principal lecturer:** Dr Ian Wassell**Taken by:** Part IA CST 50%, Part IA CST 75%**Past exam questions**

No. of lectures and practical classes: 12 + 7

Suggested hours of supervisions: 3-4

This course is a prerequisite for Operating Systems and Computer Design (Part IB), ECAD and Architecture Practical Classes (Part IB).

## Aims

The aims of this course are to present the principles of combinational and sequential digital logic design and optimisation at a gate level. The use of n and p channel MOSFETs for building logic gates is also introduced.

## Lectures

**Introduction.**Semiconductors to computers. Logic variables. Examples of simple logic. Logic gates. Boolean algebra. De Morgan’s theorem.**Logic minimisation.**Truth tables and normal forms. Karnaugh maps. Quine-McCluskey method.**Binary adders.**Half adder, full adder, ripple carry adder, fast carry generation.**Combinational logic design: further considerations.**Multilevel logic. Gate propagation delay. An introduction to timing diagrams. Hazards and hazard elimination. Other ways to implement combinational logic.**Introduction to practical classes.**Prototyping box. Breadboard and Dual in line (DIL) packages. Wiring. Use of oscilloscope.**Sequential logic.**Memory elements. RS latch. Transparent D latch. Master-slave D flip-flop. T and JK flip-flops. Setup and hold times.**Sequential logic.**Counters: Ripple and synchronous. Shift registers.**Synchronous State Machines.**Moore and Mealy finite state machines (FSMs). Reset and self starting. State transition diagrams. Elimination of redundant states.**Further state machines.**State assignment: sequential, sliding, shift register, one hot. Implementation of FSMs.**Electronics, Devices and Circuits.**Current and voltage, resistance, basic circuit theory, the potential divider. Solving non-linear circuits. Materials, semiconductors and the p-n junction, i.e., the diode. n and p channel MOSFETs and n-MOSFET logic, e.g., n-MOSFET inverter. Switching speed and power consumption problems in n-MOSFET logic. CMOS logic. Logic families. Noise margin. Analogue interfacing and operational amplifiers. [3 lectures]

## Objectives

At the end of the course students should

- understand the relationships between combination logic and boolean algebra, and between sequential logic and finite state machines;
- be able to design and minimise combinational logic;
- appreciate tradeoffs in complexity and speed of combinational designs;
- understand how state can be stored in a digital logic circuit;
- know how to design a simple finite state machine from a specification and be able to implement this in gates and edge triggered flip-flops;
- understand how to use MOSFETs to build digital logic circuits.
- understand the effect of finite load capacitance on the performance of digital logic circuits.
- understand basic analogue interfacing.

## Recommended reading

* Harris, D.M. & Harris, S.L. (2013). *Digital design and computer architecture*. Morgan Kaufmann (2nd ed.). The first edition is still relevant.

Katz, R.H. (2004). *Contemporary logic design*. Benjamin/Cummings. The 1994 edition is more than sufficient.

Hayes, J.P. (1993). *Introduction to digital logic design*. Addison-Wesley.

Books for reference:

Horowitz, P. & Hill, W. (1989). *The art of electronics*. Cambridge University Press (2nd ed.) (more analog).

Weste, N.H.E. & Harris, D. (2005). *CMOS VLSI Design - a circuits and systems perspective*. Addison-Wesley (3rd ed.).

Mead, C. & Conway, L. (1980). *Introduction to VLSI systems*. Addison-Wesley.

Crowe, J. & Hayes-Gill, B. (1998). *Introduction to digital electronics*. Butterworth-Heinemann.

Gibson, J.R. (1992). *Electronic logic circuits*. Butterworth-Heinemann.