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CSE 410Computer Systems

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Lecture 2 – Information Representation

Review: A Computer isReview:

A Computer is …

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mainmemory

processor

processor/memory bus

I/O bI/O bus

networkinterface

harddisk

video /camera

opticaldrive

serialports

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interface

disk

camera

drive

ports

BitsBits •^

All memories are composed of (billions of) bits

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A bit is:– high or low voltage– 0 or 1– true or false– yes or no– on or offIt’s all how you interpret itIt s all how you interpret it

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But to store anything complicated we use a bunch ofbits to make up a number, character, instruction, …

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Computer MemoryComputer

Memory

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All memories are organized by grouping sets of bits

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into individual memory cells

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Each cell has an

address

and its

contents

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Standard organization now: 1 cell = 8 bits = 1

byte

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A single byte can hold

A small integer (0 255 or

– A small integer (0-255 or -128-127)– A single character (‘a’, ‘A’, ‘?’, ‘#’, ‘ ’, …)– A boolean value (00000000 00000001)

A boolean value (00000000, 00000001)

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Some common storage unitsSome

common storage units

# bits

unit byte

half-word

half wordwordd^

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double word

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Terminology varies: this is how MIPS does it; the Intelx86 calls 16 bits a word & 32 bits a double-word

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AlignmentAlignment •^

An object in memory is “aligned” when its address is

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a multiple of its size

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Byte: always aligned

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Halfword: address is multiple of 2

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Word: address is multiple of 4Double word: address is multiple of 8

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Double word: address is multiple of 8

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Alignment simplifies load/store hardware– And is required by MIPS but not x

And is required by MIPS, but not x

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Binary Hex and DecimalBinary

, Hex, and Decimal

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It’s unwieldy to work with long strings of binary digits,

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so we group them in chunks of 4 and treat eachchunk as a digit in base 16H

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Hex digits:–

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9 = 1001, __ = 1010, __ = 1011

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__

, __

, __

, __

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Usual notation for hex integer in C, Java, …: 0x1c

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Hex NumbersHex

Numbers

•^

What is 0x2a5 in decimal?– 0x2a5 = 2

×

2 + a

×

×

= ________________________________

•^

What about 0xbad?

•^

What about 0xbad?_____________________

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Be sure you realize that 0x

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Binary Hex and DecimalBinary

, Hex, and Decimal

01

Binary

2

Hex

16

Binary

Hex0x30x90 A

16

0xA0xF0x

0x1F0x7F0xFF

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Binary Hex and DecimalBinary

, Hex, and Decimal

Hex

Decimal

Hex

16

Decimal

10

0x

0x

0 A

0xA

0xF

0x

0x1F

0x7F

0xFF

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Unsigned binary numbersUnsigned

binary numbers

•^

Each bit represents a power of 2

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p

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For unsigned numbers in a fixed width n-bit field:– 2

n^ distinct values

– the minimum value is 0– the maximum value is 2

n-

, where n is the number

of bits in the fieldof bits in the field

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Fixed field widths determine many limits– 5 bits = 32 possible values (

5 bits

32 possible values (

– 10 bits = 1024 possible values (

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Signed NumbersSigned

Numbers

•^

For unsigned numbers,

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– each bit position represents a power of 2– range of values is 0 to 2

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How can we indicate negative values?– two states: positive or negative

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– a binary bit indicates one of two states: 0 or 1 ⇒

use one bit for the sign bit

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Format of 32

-bit signed integer

Format of 32 bit signed integer sign bit(1 bit)

numeric value(31 bits)

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Bit 31 is the sign bit

... –^ 0 for positive numbers, 1 for negative numbers– aka most significant bit (msb), high order bit

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Example: 4

-bit signed numbers

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Hex

Bin

UnsignedDecimal

SignedDecimal

Example:

4 bit signed numbers

sign bit(1 bit)

numeric value

F E D C

numeric

value

(3 bits)

C B A 9 8

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