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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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Fundamentals of computer science part i2 l.jpg

Fundamentals of Computer SciencePart i2

Lecture 3

Digital Logic


Topics for this lecture l.jpg
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


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Microprocessor core layout

AMULET3, being designed at the University of Manchester.

Low power, high performance, asynchronous, ARM compatible.

Size 3mm x 1mm.


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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)


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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)


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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


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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


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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...


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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


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More gates (NAND)

Simpler - one type of gate…

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

Question: Can you do NOT?


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More gates (XOR)

XOR is eXclusive OR

1 only if exactlyone input is 1


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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


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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


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Clock signals

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

  • Interval between pulses = clock cycle time

  • Usually detect rising/falling edge


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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


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Memories

  • Registers

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

    • N bits = one word

  • Memories

    • M registers gives M-word memory


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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

  • 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


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Half-adder

  • 2 bits on input

  • 1 bit sum plus 1 bit carry on output

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


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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


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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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