Fundamentals of Computer Science Part i2

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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

Topics for this lecture
• Gates and Boolean logic
• AND, OR, NOT, NAND, …
• Integrated circuits
• SSI,MSI,LSI,VLSI
• Memory
• Flip-Flop
• Arithmetic

Microprocessor core layout

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...

B

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

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
• 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
• 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...