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# fundamentals of computer science part i2 - PowerPoint PPT Presentation

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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### Fundamentals of Computer SciencePart i2

Lecture 3

Digital Logic

• Gates and Boolean logic

• AND, OR, NOT, NAND, …

• Integrated circuits

• SSI,MSI,LSI,VLSI

• Memory

• Flip-Flop

• Arithmetic

AMULET3, being designed at the University of Manchester.

Low power, high performance, asynchronous, ARM compatible.

Size 3mm x 1mm.

• 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)

• 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)

• 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

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

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?

More gates (XOR)

XOR is eXclusive OR

1 only if exactlyone input is 1

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

• Combinational circuits

• Boolean functions, transform inputs to output

• Memories

• can store bits; contain feedback

• Flip-Flop

• Arithmetic

• Control

• data buses, clocks, etc

• Clock is a circuit that emits a series of pulses.

• Interval between pulses = clock cycle time

• Usually detect rising/falling edge

• 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

• Registers

• N-bit flip-flop gives N-bit register

• N bits = one word

• Memories

• M registers gives M-word memory

• 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

• 2 bits on input

• 1 bit sum plus 1 bit carry on output

• Cannot handle carry in the middle of the word...

• 2 bits andcarry on input

• 1 bit sum plus 1 bit carry on output

• Can be strung together into N-bit carry, ripple effect

• Arithmetic Logic Unit