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Computer Science

CS101 Lecture 03: Hexadecimal Numbers Text Representation

Hexadecimal Numbers Text Encoding ASCII and Unicode Aaron Stevens (azs@bu.edu) 23 January 2013

Computer Science

What You’ll Learn Today

  A great shortcut for writing binary numbers  How do computers store text information?

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Computer Science

Just Call Me!

Here’s my phone number: 000101101111111110010110010000011001!

What’s wrong with this number? !

–  Hard to write on a napkin –  Vulnerable to transcription errors –  Won’t make you popular at parties

Computer Science

Binary, Hexadecimal, Decimal

Each four bits map to a hex digit. Hexadecimal prefix 0x????

No inherent value, just means “treat as a hex number”

0x94D3

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Computer Science

Hexadecimal to Decimal

Convert each hex digit into 4 bits. Convert binary to decimal. Example: 0x94D3 = 1001 0100 1101 0011 = 215 + 212 + 210 + 27 + 26 + 24 + 21 +

20 = 32768 + 4096 + 1024 + 128 + 64 +

16 + 2 + 1 = 38099 (decimal)

Computer Science

Conversions Between Number Systems

Try some! http://www.mathsisfun.com/binary-decimal-hexadecimal-converter.html

My phone number: 0x16FF96419

(or:

0001 0110 1111 1111 1001 0110 0100 0001 1001)

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Computer Science

Binary Representations

Recall: a single bit can be either a 0 or a 1 What if you need to represent more than 2 choices? n bits can represent 2n possible combinations

Computer Science

Representing Text

A character set is a list of characters and the numbers (binary codes) used to represent each one.

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Computer Science

The ASCII Character Set

ASCII stands for American Standard Code for Information Interchange

ASCII originally used seven bits to represent each character, allowing for 128 unique characters

Later extended ASCII evolved so that all eight bits were used.

Computer Science

The ASCII Character Set (7 bits)

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Computer Science

ASCII Encoding

Example: Hello, world! H -> 0x48 -> 01001000!e -> 0x65 -> 01100101!l -> 0x6c -> 01101100!l -> 0x6c -> 01101100!o -> 0x6f -> 01101111!, -> 0x2c -> 00101100! -> 0x20 -> 00100000!w -> 0x77 -> 01110111!o -> 0x6f -> 01101111!r -> 0x72 -> 01110010!l -> 0x6c -> 01101100!d -> 0x64 -> 01100100!! -> 0x21 -> 00100001

Encoding Algorithm: For each character:  Find it’s ASCII code.  Convert to binary.

Computer Science

ASCII Decoding

01000010 01100101 00100000 01110100 01110010 01110101 01100101 00100000 01110100 01101111 00100000 01111001 01101111 01110101 01110010 00100000 01110011 01100011 01101000 01101111 01101111 01101100!

!01000010 -> 0x42 -> B!!01100101 -> 0x65 -> e!

Decoding Algorithm: For each 8 bits:  Convert Hex/decimal value  Lookup ASCII symbol

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Computer Science

ASCII Decoding

01000010 -> 0x42 -> B!01100101 -> 0x65 -> e!00100000 -> 0x20 -> !01110100 -> 0x74 -> t!01110010 -> 0x72 -> r!01110101 -> 0x75 -> u!01100101 -> 0x65 -> e!00100000 -> 0x20 -> !01110100 -> 0x74 -> t!01101111 -> 0x6f -> o!00100000 -> 0x20 -> !01111001 -> 0x79 -> y!01101111 -> 0x6f -> o!01110101 -> 0x75 -> u!01110010 -> 0x72 -> r!00100000 -> 0x20 -> !01110011 -> 0x73 -> s!01100011 -> 0x63 -> c!01101000 -> 0x68 -> h!01101111 -> 0x6f -> o!01101111 -> 0x6f -> o!01101100 -> 0x6c -> l!

Computer Science

The Extended ASCII Character Set

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Computer Science

ASCII Art

Computer Science

Can't You Take a Joke? :-)

Carnegie Mellon professor Scott E. Fahlman Proposed ASCII emoticons, Sept. 19, 1982. Source: http://www.wired.com/science/discoveries/news/2008/09/dayintech_0919

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Computer Science

Unicode Character Set

Extended ASCII is not enough for international use. Unicode uses 16 bits per character How many characters can UNICODE represent? Unicode is a superset of ASCII -- the first 256 characters

correspond exactly to the extended ASCII character set.

Computer Science Unicode Character Distribution

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Computer Science

Computer Science

What You Learned Today

More encoding!

 Hexadecimal Numbers  Character Sets   ASCII  Unicode

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Computer Science Announcements and To Do

 Homework 1 due tonight!  Readings:

  Reed ch 5, pp 83-87, 89-90 (today)

  Lab 2 on THURSDAY   Go to your scheduled lab time.   You must submit a document from the lab as evidence of

attendance!