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Chapter 2: Binary Code
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All types of information we store and manage with a computer is stored as ______.
numbers
At the lowest level, the computer stores all information using digits 0 and 1, which is also known as ______.
Binary code
What is a number?
It's a unit of an abstract mathematical system subject to the laws of arithmetic.
A number represents a ____ that certain arithmetic operations can be applied to.
value
What are the 4 categories of numbers?
1. Natural Numbers
2.Integers
3. Negative Numbers
4. Rational Numbers
What is a natural number?
It's the number o or any # obtained by repeatedly adding 1 to this number.
What is a negative number?
It's a number less than 0 AND numbers opposite in sign to a positive number.
What is an integer?
Any of natural numbers OR any of the negative of those numbers OR zero.
What is a rational number?
An integer OR the quotient of two integers----any value that can be expressed as a fraction.
We use numbers to represent other forms of data such as ____ and ____.
Characters and images.
What is the name of the number system that humans use daily?
Base-10
What is a base?
The foundational value of a number system, which dictates the number of digits and the value of digit positions.
Numbers are written using ________ ________.
Positional Notation
What is positional notation?
It is a system of expressing # in which the digits are arranged in succession, the position of each digit has a place and the # is equal to the sum of the products of each digit by its place value.
A formal way of defining positional notation is to say that a value is represented as a ______ in the ______ of the number system.
polynomial ; base
What is a polynomial?
A sum of two or more algebraic terms, each of which consists of a constant multiplied by one or more variables raised to a non negative integral power.
When defining positional notation, the _______ is at the base of the number system.
variable
Positional notation is possible only because of the concept of _____.
Zero
_____ was the fundamental concept at the intersection of all zero branches of modern mathematics.
Zero
Georges Ifrah's book was called?
"The Universal History of Computing"
Book that basically said the discovery of zero gave the human mind a powerful potential.
"The Universal History of Computing" by Georges Ifrah.
Our number system is base _____.
10
Number systems allow us to represent ______ in different ways.
values
The rightmost digit is the _____ position for ALL BASES.
"ones"
_______, a computer technique, takes numbers and scrambles them and one way to scramble numbers is to interpret them in a different base.
Hashing
What is hashing?
A computer technique, takes numbers and scrambles them and one way to scramble numbers is to interpret them in a different base.
Base 2 is ____ and it is particularly important in computer processing.
binary
What are two number systems that are powers of two?
Base 8 (octal) AND Base 16 (hexadecimal)
What is the abacus?
a device that uses positional notation to represent a decimal number.
Facts about the Abacus (NOT how it works):
-Still used today in many Asian cultures.
-Sufficient for basic business transactions.
-Skilled user can rival anyone with out calculation with BOTH speed and accuracy.
Console of IBM 650 Facts:
-Called the "Ford Tri-Motor" of computers
-Shipped to Latin American & enjoyed extended life.
What was the console of IBM 650?
It was a popular commercial computer in the late 1950s and it allowed operators to read the contents of memory using the bi-quinary system.
How does the console of IBM 650 work?
-Uses 7 lights to represent the 10 decimal digits.
-each digit is represented by 2 lights.
-If LEFT light is ON, then 0 through 4 numbers are activated (From top to bottom).
If RIGHT light is ON, then 5 through 9 numbers are activated (From top to bottom).
For bases higher than 10, we use _____ as digit.
letters
What letters to represent digits?
A - 10
B - 11
C - 12
D - 13
...and so forth...
How do you represent the 16 digits in base 17?
0,1,2,3,4,5,6,7,8,9,,A,B,C,D,E,F,G
*always stop a # before the actual # or a letter before the actual letter.
To represent the base value in any base, you need ____ digits.
2
The rules of binary arithmetic are _____.
analogous.
What is the special relationship between binary and octal numbers?
Given a number in binary, you can read it off in octal AND given a number in octal, you can read it off in binary.
What is the reason binary can be immediately converted to octal and binary to octal?
8 is a power of 2.
What is the relationship between a hexadecimal digit and binary digits?
Every hexadecimal digit can be represented in 4 binary digits.
Can you count to three?
Cognitive psychologists have demonstrated that preschool children DO NOT identify more than 3 sets:
-A set of one object, 2 objects, and 3 or more objects (aka many).
-Until so centuries ago, many languages had only two or 3 number words: "single", "pair" and "many"
How many binary digits does it take to represent each hexadecimal digit?
4
What are the rules or steps for converting base 10 numbers?
While the quotient is not zero
1. Divide the decimal # by the new base.
2. Make the remainder the next digit to the left in the answer.
3. Replace the decimal # with the quotient
What is an algorithm?
Its a logical sequence of steps that solves a problem.
A in hexadecimal is 10 in decimal and therefore _____ in binary.
1010
B in hexadecimal is 11 in decimal and therefore _____ in binary.
1011
C in hexadecimal is _____ in binary.
1100
Some of the early computers were _____ machines.
decimal
Modern computers are ______ machines.
Binary
(#'s within the computer are represented in binary form)
All information is somehow represented using BINARY values. Why?
each storage location within a computer contains either a low-voltage signal or a high-voltage signal. Since each location can ONLY have 1 or 2 states, then it is logical to equate (represent) those states to 0 and 1.
A low-voltage signal is equated with a _____ and a high-voltage signal is equated with a ______.
low= 0
high= 1
Storage location cannot be _____: it must contain either a ___ or a ___.
empty ; 0 or a 1
What is a Binary digit?
a digit in the binary number system; a 0 or a 1
What is a Bit?
a Binary digit
What is a Byte?
8 binary digits.
What is a Word?
a GROUP of 1 or more byte
The number of bits in a word is known as the _____ ______ of the computer.
world length
The same operational rule apply to other bases as they do in base ___.
10
Computer hardware is designed using numbers in base ___.
2
IBM 370 architecture in the late 1970s had:
half words (2 bytes or 16 bits)
full words (4 bytes)
double words (8 bytes)
Modern computers are often __-bit machines such as (give an example) or __-bit machines such as (give an example). However, some microprocessors that are used in applications such as pagers are __-bit machines.
32-bit ; example: Intel's Pentinum IV processor
64-bit ; example: Hewlett-Packard's Alpha processor AND Intel's Itanium 2 processor.
8-bit
what awards did Grace Murray Hopper receive?
-honorary degrees from more than 90 colleges/universities.
-the 1st Computer Sciences Man of the Year award by the
Data processing Management association.
-the Contributors to CS Education Award given by the Special Interest Group for CS Education (SIGCSE).
*which is part of ACM (Association for Computing Machinery)
In 1991, what award did Grace Murray Hopper receive?
National Medal of Technology
Rear Admiral Hopper was known as the ______________________.
"Mother of computerized data automation" in the Navy
At the time of her death, Rear Admiral Hopper was a senior consultant at ______.
Digital Equipment Corporation
What did Rear Admiral Hopper hand out to young people often?
Colored wires, which she called nanoseconds b/c they were cut to a length of about 1 foot---the distance that light travels in a nanosecond (billionth of second).
What projects did Rear Admiral Hopper work on in her lifetime?
When she joined the navy:
-programmer of Mark I @ Harvard Uni.
-Navy's Mark II and Mark III computers.
-joined Eckert-Mauchly Computer Corporation & worked on UNIVAC I
-Active in design, implementation, and use of COBOL (common business oriented language) *still used widely i business data processing.
Rear Admiral Hopper loves telling the story of when on Mark II, one of the operators discovered the first computer "____"-----a ____ caught in one of the relays.
"bug" ; moth
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