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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
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
slide3
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
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
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
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
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
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...

boolean algebra
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
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
More gates (XOR)

XOR is eXclusive OR

1 only if exactlyone input is 1

integrated circuits chips
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
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 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
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
Memories
  • Registers
    • N-bit flip-flop gives N-bit register
    • N bits = one word
  • Memories
    • M registers gives M-word memory
arithmetic
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
half adder
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
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
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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