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CS E1: Section 1:Counting in Binary
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George Boole (1815-1864)
English mathematician Invented boolean logic
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George Boole (1815-1864)
English mathematician Invented boolean logic
Boolean Logic is everywhere boolean tools are built into search engines:
Boston Public Library Google Gmail
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George Boole (1815-1864)
English mathematician Invented boolean logic
Boolean Logic is everywhere lets you search for
Boston Public Library sharks NOT attack
Gmail
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George Boole (1815-1864)
English mathematician Invented boolean logic
Boolean Logic is everywhere lets you search for
Boston Public Library sharks NOT attack
"David Malan" AND "Dan Armendariz" Gmail
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George Boole (1815-1864)
English mathematician Invented boolean logic
Boolean Logic is everywhere lets you search for
Boston Public Library sharks NOT attack
"David Malan" AND "Dan Armendariz" Gmail from:[email protected] OR from:
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Claude Shannon (1916-2001)
American Mathematician Founded circuit design at 21 with his
Master's thesis at MIT Called the "most important master's thesis
of all time"
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Claude Shannon (1916-2001)
American Mathematician Founded circuit design at 21 with his
Master's thesis at MIT Called the "most important master's thesis
of all time"
The thesis describes how Boolean logiccircuits can represent any logical ornumerical relationship
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Claude Shannon (1916-2001)
American Mathematician Founded circuit design at 21 with his
Master's thesis at MIT Called the "most important master's thesis
of all time"
The thesis describes how Boolean logiccircuits can represent any logical ornumerical relationship
(wow - that's what makes computerspossible)
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What is a function?
A function is ...
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What is a function?
A function is ...
like a "machine" that turns inputs into an output
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What is a function?
A function is ...
like a "machine" that turns inputs into an output like a "black box" - to use it we don't need to know how it
works, we just need to know what it needs (inputs) and whatit does (output)
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What is a function?
For our purposes, a function is ...
like a "machine" that turns inputs into an output like a "black box" - to use it we don't need to know how it
works, we just need to know what it needs (inputs) and whatit does (output)
repeatable. The same inputs lead to the same output.
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15/44Elements of Computing Systems, Nisan & Schocken, MIT Press, www.idc.ac.il/tecs, Chapter 1: Boolean Logic slide 10
a b out
0 0 0
0 1 0
1 0 01 1 1
How do we describe a function? With a truth table.
a and b are inputs of function"out" is the output of the function
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16/44Elements of Computing Systems, Nisan & Schocken, MIT Press, www.idc.ac.il/tecs, Chapter 1: Boolean Logic slide 10
What is the truth table of the "NOT" function?
How many inputs does it have?
NOT
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17/44Elements of Computing Systems, Nisan & Schocken, MIT Press, www.idc.ac.il/tecs, Chapter 1: Boolean Logic slide 10
a
0
1
What is the truth table of the "NOT" function?
How many inputs does it have?
ONEHow many outputs does it have?
NOT
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18/44Elements of Computing Systems, Nisan & Schocken, MIT Press, www.idc.ac.il/tecs, Chapter 1: Boolean Logic slide 10
a out
0
1
What is the truth table of the "NOT" function?
How many inputs does it have?
ONEHow many outputs does it have?
ONE
What is the relationship betweenthem?
NOT
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19/44Elements of Computing Systems, Nisan & Schocken, MIT Press, www.idc.ac.il/tecs, Chapter 1: Boolean Logic slide 10
a out
0 1
1 0
What is the truth table of the "NOT" function?
How many inputs does it have?
ONEHow many outputs does it have?
ONE
What is the relationship betweenthem?
OPPOSITE
NOT
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Elements of Computing Systems, Nisan & Schocken, MIT Press, www.idc.ac.il/tecs, Chapter 1: Boolean Logic slide 10
a b out
0 0
0 1
1 01 1
What is the truth table of the "OR" function?
How many inputs does it have?
TWOHow many outputs does it have?
ONE
What is the relationship betweenthem?
OR
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Elements of Computing Systems, Nisan & Schocken, MIT Press, www.idc.ac.il/tecs, Chapter 1: Boolean Logic slide 10
a b out
0 0 0
0 1
1 01 1
What is the truth table of the "OR" function?
How many inputs does it have?
TWOHow many outputs does it have?
ONE
What is the relationship betweenthem?
OR
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Elements of Computing Systems, Nisan & Schocken, MIT Press, www.idc.ac.il/tecs, Chapter 1: Boolean Logic slide 10
a b out
0 0 0
0 1 1
1 01 1
What is the truth table of the "OR" function?
How many inputs does it have?
TWOHow many outputs does it have?
ONE
What is the relationship betweenthem?
OR
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Elements of Computing Systems, Nisan & Schocken, MIT Press, www.idc.ac.il/tecs, Chapter 1: Boolean Logic slide 10
a b out
0 0 0
0 1 1
1 0 11 1
What is the truth table of the "OR" function?
How many inputs does it have?
TWOHow many outputs does it have?
ONE
What is the relationship betweenthem?
OR
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Elements of Computing Systems, Nisan & Schocken, MIT Press, www.idc.ac.il/tecs, Chapter 1: Boolean Logic slide 10
a b out
0 0 0
0 1 1
1 0 11 1 1
What is the truth table of the "OR" function?
How many inputs does it have?
TWOHow many outputs does it have?
ONE
What is the relationship betweenthem?
OR
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Elements of Computing Systems, Nisan & Schocken, MIT Press, www.idc.ac.il/tecs, Chapter 1: Boolean Logic slide 10
a b out
0 0 0
0 1 1
1 0 11 1 1
What is the truth table of the "OR" function?
How many inputs does it have?
TWOHow many outputs does it have?
ONE
What is the relationship betweenthem?
TRUE IF EITHER ORBOTH ARE TRUE,
FALSE OTHERWISE
OR
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Elements of Computing Systems, Nisan & Schocken, MIT Press, www.idc.ac.il/tecs, Chapter 1: Boolean Logic slide 3
All Boolean functions of 2 variables
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Elements of Computing Systems, Nisan & Schocken, MIT Press, www.idc.ac.il/tecs, Chapter 1: Boolean Logic slide 3
All Boolean functions of 2 variables
What do you notice aboutthe pattern?
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Elements of Computing Systems, Nisan & Schocken, MIT Press, www.idc.ac.il/tecs, Chapter 1: Boolean Logic slide 5
Gate logic - each function has its own "chip" inside the cpu
Gate logic a gate architecture designed to implement a Boolean function
Elementary gates:
Composite gates:
Important distinction: Interface (what) VS implementation (how).
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CS E1, Section 1:number vocabularybit, byte, kilo-, mega-, giga-, tera-
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Vocab
BIT
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Vocab
BIT a one or a zero
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Vocab
BIT a one or a zero
BYTE
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Vocab
BIT a one or a zero
BYTE eight bits: 0 0 0 0 0 0 0 0
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Vocab
BIT a one or a zero
BYTE eight bits: 0 0 0 0 0 0 0 0
can store 2^8 numbers:
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Vocab
BIT a one or a zero
BYTE eight bits: 0 0 0 0 0 0 0 0
can store 2^8 numbers: 0-255 KILOBYTE
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Vocab
BIT a one or a zero
BYTE eight bits: 0 0 0 0 0 0 0 0
can store 2^8 numbers: 0-255 KILOBYTE
~1000 bytes
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Vocab
BIT a one or a zero
BYTE eight bits: 0 0 0 0 0 0 0 0
can store 2^8 numbers: 0-255 stores one character
KILOBYTE ~1000 bytes actually 2^10 numbers: 0-1023
stores less than eight twitter posts
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Vocab
BIT a one or a zero
BYTE eight bits: 0 0 0 0 0 0 0 0
can store 2^8 numbers: 0-255 stores one character
KILOBYTE ~1000 bytes actually 2^10 numbers: 0-1023
stores less than eight twitter posts MEGABYTE
~1,000,000 bytes actually 2^30 numbers: 0-1,048,575 - less than 1/3 of
a typical mp3 song
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Vocab
http://en.wikipedia.org/wiki/Megabyte
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CS E1, Section 1:asciiAmerican Standard Code for Information
Interchange
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CS E1, Section 1: ascii
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Ascii numbers to remember:
65 is capital 'A'97 is lowercase 'a'
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Source, explanation: link
http://www.hanselman.com/blog/WhyTheAskObamaTweetWasGarbledOnScreenKnowYourUTF8UnicodeASCIIAndANSIDecodingMrPresident.aspx8/9/2019 Section1 Nore
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example: ascii in a spreadsheet
https://docs.google.com/spreadsheet/ccc?key=0ApKUsT5wTHHgdHpDNkEtOUlDUUNkeVF4cmlhSlVXYVE&
hl=en_US
https://docs.google.com/spreadsheet/ccc?key=0ApKUsT5wTHHgdHpDNkEtOUlDUUNkeVF4cmlhSlVXYVE&hl=en_UShttps://docs.google.com/spreadsheet/ccc?key=0ApKUsT5wTHHgdHpDNkEtOUlDUUNkeVF4cmlhSlVXYVE&hl=en_UShttps://docs.google.com/spreadsheet/ccc?key=0ApKUsT5wTHHgdHpDNkEtOUlDUUNkeVF4cmlhSlVXYVE&hl=en_UShttps://docs.google.com/spreadsheet/ccc?key=0ApKUsT5wTHHgdHpDNkEtOUlDUUNkeVF4cmlhSlVXYVE&hl=en_UShttps://docs.google.com/spreadsheet/ccc?key=0ApKUsT5wTHHgdHpDNkEtOUlDUUNkeVF4cmlhSlVXYVE&hl=en_US
