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Fundamentals of Computer Science Part i2PowerPoint Presentation

Fundamentals of Computer Science Part i2

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Fundamentals of Computer Science Part i2. Lecture 3 Digital Logic. Topics for this lecture. Gates and Boolean logic AND , OR , NOT , NAND , … Integrated circuits SSI,MSI,LSI,VLSI Memory Flip-Flop Arithmetic Half-adder, Full-adder. Microprocessor core layout.

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Topics for this lecture

- Gates and Boolean logic
- AND, OR, NOT, NAND, …

- Integrated circuits
- SSI,MSI,LSI,VLSI

- Memory
- Flip-Flop

- Arithmetic
- Half-adder, Full-adder

AMULET3, being designed at the University of Manchester.

Low power, high performance, asynchronous, ARM compatible.

Size 3mm x 1mm.

Basics of hardware design

- Components in the picture
- data path (bottom strip), register bank (centre)
- ALU, adder, multiplier, instruction controller, ...

- The lowest logical design level
- gates built from transistors
- circuits built from gates (arithmetic, memory)

- Device level, physics...
- N/P-type semiconductors (transistors)

Digital circuits

- Two values only, 0 and 1
- continuous voltage range (within bounds)
- 0 is low signal (voltage range 0 to 1)
- 1 is high signal (voltage range 2 to 5)

- Gates
- electronic devices that compute functions of 0/1
- made from transistors (very fast & small switches)

How a transistor works...

- When input voltage below threshold, no current flows through; then output voltage high
- When input voltage above threshold, current flows through; then output voltage low

Note signal is inverted, hence a NOT gate

The three main gates

A, B inputs X output

X = f(A,B)

(truth table)

NOTinvert (negate) single input.

AND 1 only if both inputs 1

OR 1 if at least one input 1

Two more gates

NAND

0 only if both inputs 1 (inverted AND)

NOR

0 if at least one input 1

(inverted OR)

Simpler - 2 instead of 3 transistors...

A

A

A

C

Boolean algebra- Can have functions of N variables, eg
M = f (A,B,C)

- Write
AB for A AND B

A+B for A OR B

for NOT A

- Write functions as expressions
M = BC + A C + AB + ABC (majority vote)

- Laws to identify equivalent functions, eg
A + BC = (A+B)(A+C) A = 0

More gates (NAND)

Simpler - one type of gate…

NAND is complete (any circuit can be created from it)

Question: Can you do NOT?

Integrated circuits (chips)

SSI chip

5mm x 5mm

Standardised

Pins

Classification based on number of gates:

from Small Scale Integrated (SSI), 1-10 gates,

to Very Large Scale Integrated (VLSI), > 100,000 gates

Types of chips

- Combinational circuits
- Boolean functions, transform inputs to output

- Memories
- can store bits; contain feedback
- Flip-Flop

- Arithmetic
- Half-adder, Full-adder

- Control
- data buses, clocks, etc

Clock signals

- Clock is a circuit that emits a series of pulses.
- Interval between pulses = clock cycle time
- Usually detect rising/falling edge

The Flip-Flop

- Also called a clocked D latch
- Has inputs D and clock, and output Q
- When control is on, Q = D
- When control is off, output cannot change, & hence D stored

Memories

- Registers
- N-bit flip-flop gives N-bit register
- N bits = one word

- Memories
- M registers gives M-word memory

Arithmetic

- Addition
- 1-bit addition yields 1-bit result and 1-bit carry
0 + 0 = 0

0 + 1 = 1

1 + 0 = 1

1 + 1 = 0 carry 1

- 1-bit addition yields 1-bit result and 1-bit carry
- Adders
- half-adder = 1-bit adder with 2 bit input
- full-adder = 1-bit adder with additional carryinput
- N-bit adder requires N full-adders

Half-adder

- 2 bits on input
- 1 bit sum plus 1 bit carry on output
- Cannot handle carry in the middle of the word...

Full-adder

Built from twohalf-adders

- 2 bits andcarry on input
- 1 bit sum plus 1 bit carry on output
- Can be strung together into N-bit carry, ripple effect

Summary

- Arithmetic Logic Unit
- similar to adders

- Data bus
- transfers data along wires, one wire per bit
- using control signals (clocks)

- More complex circuits
- design in Boolean algebra
- build from standard chips or produce VLSI

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