Understanding
Binary Numbers
Introduction:
Understanding Binary Numbers
1 of 7
Elements
Introduction
When working with Digital Media, it’s
imperative that you posses a basic
understanding of how computers save,
transfer, and process data. In order to
visualize and conceptualize this
information students should first build
and understanding of the binary number
system.
The Matrix Movie Clip
Introduction:
Understanding Binary Numbers
1 of 7
Elements
Introduction
If you have ever seen the movie “The
Matrix” and enjoyed thinking about how it
all works; jumping in and out of a
computer program etc… Then you know
something about conceptualizing.
To form (a concept or concepts) out of
observations, experience, data, etc.
When you use your brain to visualize
something that is abstract or on the
surface a bit difficult to see in your mind.
Understanding Binary Numbers
The binary number system,
also called the base-2 number
system, is a method of
representing numbers by using
combinations of only two
numerals: zero (0) and one (1).
Computers use the binary
number system to manipulate
and store all of their data
including numbers, words,
videos, graphics, and music.
Learning Objective:
After this lesson students should be able to:
1. Briefly explain what binary numbers are.
2. Briefly explain what decimal numbers are.
3. Explain why we need to understand binary
numbers.
4. Count with binary numbers.
5. Convert decimal numbers to binary.
6. Convert binary numbers to decimal.
7. Demonstrate an expanded vocabulary.
8. Understand the history of Binary numbers.
Pre-Assessment
2 of 7
Elements
Assess
Binary Numbers Pre Test.docx
• In 1854, British mathematician George
Boole published a landmark paper
detailing an algebraic system of logic that
would become known as Boolean
algebra.
• His logical calculus was to become
instrumental in the design of digital
electronic circuitry.
History of Binary
• In November 1937, George Stibitz, then
working at Bell Labs, completed a relaybased computer he dubbed the "Model
K" (for “Kitchen", where he had
assembled it), which calculated using
binary addition. Bell Labs thus authorized
a full research program in late 1938 with
Stibitz at the helm.
History of Binary
• Who can guess when the first machine
was able to send data over a phone line?
History of Binary Numbers
• Their Complex Number Computer,
completed January 8, 1940, was able to
calculate complex numbers. In a
demonstration to the American
Mathematical Society conference at
Dartmouth College on September 11,
1940, Stibitz was able to send the
Complex Number Calculator remote
commands over telephone lines by a
teletype. It was the first computing
machine ever used remotely over a
phone line.
History of Binary
• Model K The first Relay Based Computer
to use Binary Numbers (1937)
Decimal Number System
• What is our number base?
• What do we count by?
Decimal Number System
• Decimal notation is the writing of
numbers in a base-10 numeral system.
Examples are Roman numerals, Brahmi
numerals, and Chinese numerals, as well
as the Hindu-Arabic numerals used by
speakers of English.
What is Binary
• The binary numeral system, or base-2
number system represents numeric
values using two symbols (Numbers),
usually 0 and 1. More specifically, the
usual base-2 system is a positional
notation with a radix of 2.
• Owing to its straightforward
implementation in digital electronic
circuitry using logic gates, the binary
system is used internally by all modern
computers.
Binary reads backwards
• Normally we count from left to right,
• 1 2 3 4 etc.
• In Binary we count in the opposite
direction 8 4 2 1
• It’s important to remember this in order to
convert your numbers.
Why do we need to know about Binary?
• It is the building block of all data
• In order to understand storage capacity
and sizes, you need to know how data is
read and saved
• The data is fragile, each digit is need to
be whole
Files Read/Write
• When you save a word document the
computer will sequence the data in
binary form. Each string of digits
represent a certain value such as a
letter, space, underlined etc.
• Each program has a certain way that it
reads and writes data, all of it is written in
Binary.
Understanding Binary
Decimal 1
Binary 0001
off
off
off
on
Understanding Binary
Decimal 2
Binary 0010
off
off
on
off
Understanding Binary
Decimal 3
Binary 0011
off
off
on
on
Understanding Binary
Decimal 4
Binary 0100
off
off
on
on
Understanding Binary
Decimal 5
Binary 0101
off
on
off
on
Understanding Binary
0101
off
on
off
on
Each Number is doubled
128 64 32 16 8 4 2 1 2^8 2^6 2^5 2^4
512
256
128
64
32
16
8
4
2
1
2^3 2^2 2^1 2^0 Two to the power of
524288
262144
131072
65536
32768
16384 8192
4096 2048 1024
three
(2)(2)(2)
2*2*2
2X2X2
Boardwork
• Lets express a few numbers in Binary:
•
•
•
•
130
25
43
85
• 1312
• 2204