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Week 4 Number Systems

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Page 1: Week 4 Number Systems. Large numbers in metric Bytes The bits in a computer are grouped into larger units. A group of eight bits is called a byte. A

Week 4

Number Systems

Page 2: Week 4 Number Systems. Large numbers in metric Bytes The bits in a computer are grouped into larger units. A group of eight bits is called a byte. A

Large numbers in metric

Page 3: Week 4 Number Systems. Large numbers in metric Bytes The bits in a computer are grouped into larger units. A group of eight bits is called a byte. A

Bytes

The bits in a computer are grouped into larger units.

A group of eight bits is called a byte. A byte can be used to store 2^8 values - 256

different values. These values can be numeric values or alphanumeric values.

Page 4: Week 4 Number Systems. Large numbers in metric Bytes The bits in a computer are grouped into larger units. A group of eight bits is called a byte. A

Question

Page 5: Week 4 Number Systems. Large numbers in metric Bytes The bits in a computer are grouped into larger units. A group of eight bits is called a byte. A

Large Numbers

Page 6: Week 4 Number Systems. Large numbers in metric Bytes The bits in a computer are grouped into larger units. A group of eight bits is called a byte. A

ASCII

When bytes are used to hold characters a code must be used to represent which numeric value will represent which character.

The most common code is the American Standard Code for Information Interchange(ASCII).

One byte can hold one character.

Page 7: Week 4 Number Systems. Large numbers in metric Bytes The bits in a computer are grouped into larger units. A group of eight bits is called a byte. A

ASCII (Contd)

The letters of the alphabet and the ten characters 0 to 9 are called alphanumeric

When there are a number of characters stored together they are called strings of characters.

In ASCII the code for the letter A is 6510 or 4116.

In ASCII the code for the string of Alphanumeric Characters 36 is the ASCII code for 3 followed by the ASCII code for 6.

Page 8: Week 4 Number Systems. Large numbers in metric Bytes The bits in a computer are grouped into larger units. A group of eight bits is called a byte. A

ASCII (Contd)

The ASCII code for 3 is 5110 or 3316

The ASCII code for 6 is 5410 or 3616 Therefore it takes two bytes of memory to

store the alphanumeric string 36, one byte for each character. Contrast this with the numeric value for 3610 which is 2416

Page 9: Week 4 Number Systems. Large numbers in metric Bytes The bits in a computer are grouped into larger units. A group of eight bits is called a byte. A

Contd

When a byte is used to represent a number, the 256 different byte values can either be interpreted as all positive numbers ranging from 0 to 25510.

To allow for negative numbers, the possible range can be divided in half to allow for representation of negative and positive numbers ranging from -12810 through +12710.

Page 10: Week 4 Number Systems. Large numbers in metric Bytes The bits in a computer are grouped into larger units. A group of eight bits is called a byte. A

Contd

All positive are referred to as unsigned numbers

0 to 25510

Positive and Negative are referred to as signed

-12810 to + 12710

A typical 1 byte register in a computer may look like the one below.

Page 11: Week 4 Number Systems. Large numbers in metric Bytes The bits in a computer are grouped into larger units. A group of eight bits is called a byte. A

Contd If the number is unsigned then the largest

number that can be represented is 25510 or 28 -1

Why ? There are 256 possible values in the range 0 to 255.

If the number is signed then bit 8, (2^7), the most significant bit, is reserved as the sign bit.

Page 12: Week 4 Number Systems. Large numbers in metric Bytes The bits in a computer are grouped into larger units. A group of eight bits is called a byte. A

Contd The sign bit tells whether the number is (+),

positive, or whether the number is (-), negative.

A “0” in the sign bit means that the number is positive.

A “1” in the sign bit means that the number is negative.

Page 13: Week 4 Number Systems. Large numbers in metric Bytes The bits in a computer are grouped into larger units. A group of eight bits is called a byte. A

WORD

To handle larger numbers, several bytes are used together as a unit, often called a word.

For different computers, different meanings are given to the term word but it could represent either 2 bytes (16 bits) or four bytes (32 bits) or 8 bytes (64 bits).

Page 14: Week 4 Number Systems. Large numbers in metric Bytes The bits in a computer are grouped into larger units. A group of eight bits is called a byte. A

Word (Contd)

A two byte word has 2^16 different possible values.

The 16 bit word can be used to store unsigned numbers with a range through 0 to 65,53510.

Therefore the largest unsigned number available using 2 bytes is (2^16 -1).

Page 15: Week 4 Number Systems. Large numbers in metric Bytes The bits in a computer are grouped into larger units. A group of eight bits is called a byte. A

Extended ASCII

8 Bit code also known as Latin 1. Mostly Latin letters and accents and diacritical

marks used for example in French and German.

Problem: Russian and Arabic have totally different alphabets.

Page 16: Week 4 Number Systems. Large numbers in metric Bytes The bits in a computer are grouped into larger units. A group of eight bits is called a byte. A

Code Page

A set of 256 characters for a particular language or group of languages.

EG. International standard (I.S) 8859-2 handles Latin based Slavic Languages- Czech, Polish and Hungarian.

E.G. International standard (I.S) 8859-3 handles the characters needed For Turkish , Maltese, Esperanto and Galician.

Page 17: Week 4 Number Systems. Large numbers in metric Bytes The bits in a computer are grouped into larger units. A group of eight bits is called a byte. A

Code Page

Problem: it is impossible to mix languages on different pages.

### Does not cover Japanese or Chinese.

Page 18: Week 4 Number Systems. Large numbers in metric Bytes The bits in a computer are grouped into larger units. A group of eight bits is called a byte. A

UNICODE

Unicode is replacing ASCII as the coding standard for characters.

The basic idea to assign every character and symbol a unique 16 bit value called a code point. If you have a 16 bit code how many symbols can you represent?

Page 19: Week 4 Number Systems. Large numbers in metric Bytes The bits in a computer are grouped into larger units. A group of eight bits is called a byte. A

Contd

As the world's languages contain roughly 200,000 symbols, code points are a scarce resource. The resource must be carefully guarded and assigned with care.

Problem: Chinese and Japanese have fewer code points

allocated than symbols needed. Many are not happy with compromises that have been made.

Page 20: Week 4 Number Systems. Large numbers in metric Bytes The bits in a computer are grouped into larger units. A group of eight bits is called a byte. A

ASCII Problem

• While computers can represent 256 names for letters, no one agrees on what letters the numbers 128-256 stand for.

• That’s why your Mac Cayuga font shows up as gibberish on a Windows computer.– The number ‘250’ doesn’t mean the same thing

on a Mac as it does on a Windows PC.

Page 21: Week 4 Number Systems. Large numbers in metric Bytes The bits in a computer are grouped into larger units. A group of eight bits is called a byte. A

UNICODE, Fixing ASCII Problem

• Unicode aims to provide a unique name for every letter ever used…on the planet.

• It has room for 1,000,000 names.• Everyone agrees on what letters the names

stand for.– Technical details not discussed here: getting from

names like ‘U+0061’ to the letter ‘a’ on your computer.

Page 22: Week 4 Number Systems. Large numbers in metric Bytes The bits in a computer are grouped into larger units. A group of eight bits is called a byte. A

UNICODE, Advantages

• (Not quite yet, but in the near future) when you type in Cayuga, it will appear as Cayuga on any other computer.

• The same goes for web pages…

Page 23: Week 4 Number Systems. Large numbers in metric Bytes The bits in a computer are grouped into larger units. A group of eight bits is called a byte. A

Task for you

Unicode version 4 incorporates a 32 bit code version and therefore can now represent all of the world's characters in it's character coding system.

The Unicode URL is: http://www.unicode.org/ If you wish to research this further.

Page 24: Week 4 Number Systems. Large numbers in metric Bytes The bits in a computer are grouped into larger units. A group of eight bits is called a byte. A

Thank You


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•Multiple-byte data · • A byte is composed of 8 bits. Two nibbles make up a byte. • Halfwords, words, doublewords, and quadwords are composed of bytes as shown below: Bit Nibble

CS429: Computer Organization and Architecture - Bits and Bytesbyoung/cs429/slides2-bits-bytes.pdf · Byte-Oriented Memory Organization Conceptually, memory is a very large array of

Bits, Bytes, and Integers – Part 1213/lectures/02-bits-ints-part1.pdf · 2019-05-22 · ⬛Byte = 8 bits Binary 000000002 to 111111112 Decimal: 010 to 25510 Hexadecimal 0016 to

Http://proglit.com/. bits and text BY SA byte (the size of a cell of addressable memory) 8 bits on all modern systems octet = 8 bits

1 Meg Bits x 16 Bits x 4 Banks (64-MBIT) …NC UDQM CLK CKE NC A11 A9 A8 A7 A6 A5 A4 GND WE Write Enable LDQM x16 Lower Byte, Input/Output Mask UDQM x16 Upper Byte, Input/Output Mask

BITS, BYTES, AND INTEGERSwitchel/429/lectures/02-bits... · 2012-09-06 · 3 Encoding Byte Values Byte = 8 bits Binary 00000000 2 to 11111111 2 Decimal: 0 10 to 255 10 Hexadecimal

Bits and Bytes January 17, 2002 Topics Why bits? Representing information as bits –Binary/Hexadecimal –Byte representations »numbers »characters and strings

Procedures, Parameters, Values and VariablesC Types Type Stores Size char a single byte, holds one ASCII character 8 bits int An Integer 32 bits short An Integer 16 bits long An Integer

Data Encoding CTPS 2018 - intranet.cb.amrita.edu · Byte to Terabyte • Bits can be grouped together to make them easier to work with. • A group of 8 bits is called a byte. Other

OttO Vector - 5 Bits To Byte [Digital Booklet]

“The Class That Gives CMU Its Zip!” Bits and Bytes Aug. 29 ... · Bits and Bytes Aug. 29, 2002 Topics Why bits? Representing information as bits Binary/Hexadecimal Byte representations

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“2 bits, 4 bits, 6 bits a byte!” Other bits 4-1-1 ...csbio.unc.edu/mcmillan/Comp411F18/Lecture02.pdf08/24/2018 Comp 411 - Fall 2018 4-1-1: Information Please Representing Information

© A+ Computer Science - ...byte 8 bits -128 to 127 short 16 bits -32768 to 32767 int 32 bits -2 billion to 2 billion long 64 bits -big to +big float 32 bits -big to +big double 64

Java Fundamentals - kau.edu.sa · Java’s Eight Primitive Data Types DATA TYPE SIZE MIN VALUE MAX VALUE byte 8 bits ‐128 127 short 16 bits ‐32768 32767 int 32 bits –2147483648

Bits and Bytes Topics Why bits? Tell me Representing information as bits Binary/Hexadecimal Byte representations »numbers »characters and strings »Instructions

Bits and Bytes January 15, 2004 Topics Why bits? Representing information as bits Binary/Hexadecimal Byte representations »numbers »characters and strings

“2 bits, 4 bits, 6 bits a byte!” Other bits 4-1-1 ...csbio.unc.edu/mcmillan/Comp411F17/Lecture02.pdf · Special "control" characters set upper two bits to 00 ex. cntl-g → bell,

Local interconnect - Sisoog...o The LIN protocol is byte oriented. o data is sent one byte at a time. o One byte field contains a start bit (dominant), 8 data bits and a stop bit (recessive)

PowerPoint Presentation to Accompany - UCRgusta/vistech/VT_2e_ch01_ppt.pdf · Bits%and%Bytes% Visualizing ... 8 bits = 1 byte ! Binary code has two possible states: on/ off, 1/0,

DICOM PS3.5 2014a2014b - Data Structures and Encodingdicom.nema.org/medical/dicom/2014b/output/pdf/part05_changes.pdf · Sample Pixel Data Byte Streams for 8-bits Allocated and 8-bits

Chapter 4 Bits and Bytes · 2012-01-31 · Page 1 Chapter 4 Bits and Bytes • Why bits? • Representing information as bits –Binary/Hexadecimal –Byte representations • Representing

Computer Systems Organization · Computer Systems Organization Primary Memory Today Memory cells contain 8 bits. { Byte = smallest addressable memory unit. Bytes are grouped to words

Question! 01000001 1 Byte = 8 bits ASCII Code American Standard Code for Information Interchange

Bits, Bytes, Files, Hard Drives. Bits, Bytes, Letters and Words ● Bit – single piece of information ● Either a 0 or a 1 ● Byte – 8 bits of information

REST OF THE COMPUTER BEFORE THE INTERNET. Understand Your Computer Bit Binary digit 0 or 1 Byte 8 bits Unique combinations of 8 bits of 0s

Bits and Bytes September 2, 2004 Topics Why bits? Representing information as bits Binary / Hexadecimal Byte representations »Numbers »Characters and strings

ROM CPU CMOS HARD DRIVERAM. POWER on off 1 bit 8 bits = 1 byte

Features - Silicon Labs · Features: - > 4000 bits of configurations - Can be configured through SMBus or hard coded ... (6:0) Byte offset for byte read or byte wr ite operation

Bits and Bytesarcs.skku.edu/.../Courses/ComputerSystems/02.1_Bits_Bytes_BinRep.pdfExamples (char type => 1 byte, 8 bits) ... Variable x has 4-byte representation 0x01234567 ... Word

Big Data & Hadoop By Mr.Nataraj smallest unit is bit 1 byte=8 bits 1 KB (Kilo Byte)= 1024 bytes =1024*8 bits 1MB (Mega Byte)=1024 KB=(1024)^2 * 8 bits

Bits and Bytes CS 213 Aug. 27, 1998 Topics Why bits? Representing information as bits –Binary/Hexadecimal –Byte representations »numbers »characters and

QUESTION 1....Byte 1 Byte 2 The location is indicated by the setting of one of the seven bits in byte 1. For example, location 4 is indicated by setting bit 4. Bit 0 of byte 1 acts

Multibeam antennas planning— limitations and solutions...• Each neighbor QRXLEVMIN that deviates from serving cell, 1 byte (8 bits) • Use of QOFFSET, 1 byte (8 bits) • Header: