Bits, Bytes, and Beyond:
An Introduction
Prof. Dr. Mirco Schoenfeld
Learning objective
My learning objective for you:
- Theory
- Competency
Learning objective
- Theory
- From theory we learn what computers are capable of
- We also learn what they can not do well
- Many concepts have practical applications
- Competency
- You will learn to understand abstract concepts
- You will learn to think like a computer scientist
Learning by doing
What do you expect from this course?
What do you expect from this course?
Let’s get
started
Exploring “Bits, Bytes, and Beyond”
Bits
Computers are digital.
That means they have two states.
Bits
Haaschreck
(2022)
Bits
Smallest unit of information is called a Bit.
Bits
One bit alone doesn’t store much information.
We use sequences of bits to store more.
Bits
| 00 |
earth |
| 01 |
water |
| 10 |
fire |
| 11 |
air |
Bits
2 bits distinguish 4 things;
3 bits distinguish 8 things;
8 bits, distinguish 256 things.
Bits
How many things can we distinguish
using a bit sequence of
length n?
Bytes
A bit sequence of length 8 is called a Byte.
A bit sequence of length 8192 is called a Kilobyte (kB).
One Kilobyte consists of \(1024 =
2^{10}\) Byte.
Bytes
Wait, a kilo-byte has 1024 Bytes? Doesn’t kilo mean
1000?
If you need to precisely refer to 1024 Bytes, say
kibibyte.
Kibi means Kilo + Binary.
Bytes
What other names of bit sequences of a certain length do you
know?
Beyond
Let’s use these sequences to encode information.
Beyond
How can we represent whole numbers using bit
sequences?
Does your scheme support negative numbers?
Beyond
How can we represent texts using bit sequences?
Beyond
| 00 |
E (earth) |
| 01 |
W (water) |
| 10 |
F (fire) |
| 11 |
A (air) |
Beyond
How can we encode
“Hello class!”
And how many bits should we use per sign?
ASCII
Shabaz1000
(2024)
Encoding
Some available encodings:
Beyond
How can we encode images?
Image encoding
How can we encode this image?
Tantau
(2016)
Image encoding
How can we encode this image?
Tantau
(2016)
Image encoding
How can we encode this image?
Tantau
(2016)
Quick summary
Computers store everything as bit sequences.
| Bit |
Binary Digit / 0 or 1 |
not much |
| Byte |
8 Bits |
Letters in latin alphabet |
| Kilobyte (kB) |
1024 Byte or 1000 Byte |
small icon, half page of text |
| Megabyte (MB) |
1024 kB or 1000 kB |
a book, a minute of musik, a second of HD-movie |
| Gigabyte (GB) |
1024 MB or 1000 MB |
a move, a genome |
| Terabyte (TB) |
1024 GB or 1000 GB |
Wikipedia |
| Kibibyte |
always 1024 Byte |
|
Where do we go from
here?
Algorithms
In this lecture, we want to learn about algorithms.
Algorithms
Al-Jabr, or
“The Compendious Book on Calculation”
Al-Khwarizmi (820AD)
Algorithms
Lovelace describes an algorithm to compute Bernoulli numbers in her
notes to Babbage’s lecture notes in 1842.
Lovelace
(1842)
Algorithms
It is considered to be the first published algorithm ever
specifically tailored for implementation on a computer.
Lovelace
(1842)
Algorithms: A definition
Algorithms are finite sequences of instructions,
typically used
to solve specific problems.
Algorithms: escape the maze
Escape the maze!
Algorithms vs. Programs
Algorithms
- abstract description
- hardware independent
- language agnostic
Programs
- concrete list of instructions
- written in a specific language
- solve exactly one problem
Structure of algorithms
The vast majority of algorithms use variants of control
instructions:
Specifications
Problems can only be solved in a meaningful
way if the problem is
clearly defined.
A “clear problem definition”
is called a
specification.
Specifications
Specifications should answer the following comprehensively:
- what are the relevant framework conditions?
- which tools and basic operations are permitted?
- when is a solution correct or at least acceptable?
Aim of this lecture
Aim of this lecture
- We want to learn basic principles of computer
science
- We want to understand algorithms and their
complexity
- We want to understand how algorithms can be
improved
Acknowledgement
Acknowledgement:
This script is inspired by Tantau (2016).
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