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Paper 2: Digital Electronics

This Paper 2 course is taken by Part IA Computer Science Tripos students only.

*Lecturer: Dr I.J. Wassell*

*No. of lectures and practical classes:* 11 + 7

*This course is a prerequisite for Operating Systems I and ECAD (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 transistors for building 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.**Number representation.**Unsigned binary numbers. Octal and hexadecimal numbers. Negative numbers and 2's complement. BCD and character codes. Binary adders.**Combinational logic design: further considerations.**Multilevel logic. Gate propagation delay. An introduction to timing diagrams. Hazards and hazard elimination. Fast carry generation. Other ways to implement combinational logic.**Introduction to practical classes.**Prototyping box. Breadboard and Dual in line (DIL) packages. Wiring.**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.**Further state machines.**State assignment: sequential, sliding, shift register, one hot. Implementation of FSMs.**Circuits.**Solving non-linear circuits. Potential divider. N-channel MOSFET. N-MOS inverter. N-MOS logic. CMOS logic. Logic families. Noise margin. [2 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 MOS transistors

**Recommended reading**

* Harris, D.M. & Harris, S.L. (2007). Digital design and computer architecture. Morgan Kaufmann.

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.

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