Chapter 3 Data Representation
Hexadecimal
Assembly (machine) language programs for most computers use_____ notation to represent memory address values.
double-precision
Many computers implement ___________ numeric data types to increase accuracy and prevent overflow and underflow.
Segmented Memory Model
Most Intel CPUs use the ____in which each memory address is represented by two integers.
Similar to scientific notation, except that 2 is the base
What is floating point notation?
Overflow is when the result of an equation is too large in bit, to be able to fit into the data format. Underflow is when the negative exponent, the number of decimal places, is too large to fit within the data format. The probability of their occurrence be minimized is by allocating enough bit positions for data storage.
What is overflow? What is underflow? How can the probability of their occurrence be minimized?
Is an eight-bit character encoding used mainly on IBM mainframe and IBM midrange computer operating system.
What is the EBCDIC coding system?
Overflow is when the result of an equation is too large in bit, to be able to fit into the data format. If we assume the number of digits is limited then numbering systems with larger bases have greater numeric range
What is the connection between numeric range and overflow?
Overflow is when the result of an equation is too large in bit, to be able to fit into the data format. Underflow is when the negative exponent, the number of decimal places, is too large to fit within the data format.
What is the connection between range, overflow and underflow?
ASCII-7: 7 bits are used per character. This makes a character set 2^7 or 128. ASCII-8: used 8 bits per character. Makes 2^8 or 258 characters.
What is the difference between ASCII-7 and ASCII-8?
holds the bits that are interpreted to derive the real number's digits. indicates the radix point's position.
What is the mantissa and exponent of a number?
the bit in a binary number that is of the greatest numerical value. the bit in a binary number that is of the lowest numerical value.
What is the most significant bit? least significant bit?
Floating-point
_____ notation encodes a real number as a mantissa multiplied by a power (exponent) of 2.
Overflow
__________ occurs when the result of an arithmetic operation exceeds the number of bits available to store it.
Double Linked List
An element in a(n)_____ contains pointers to both the next and previous list elements.
Linked list or index
A set of data items that can be accessed in a specified order by using pointers is called a(n) ___
byte, bits
A(n) ____ contains 8 ____
Boolean
A(n) ______ data item can contain only the values true or false.
record
A(n) ______ is a data structure composed of other data structures or primitive data elements, commonly used as a unit of input and output to and from files or databases.
Array
A(n) ______ is a sequence of primitive data elements stored in sequential storage locations
index
A(n) ______ is an array of data items, each of which contains a key value and a pointer to another data item.
singly linked list
A(n) _______ stores one pointer with each list element.
Class
A(n) __________ is a data structure containing both static data and methods.
Object
A(n) __________ is one instance or variable of a class.
Data structure
A(n)_____ is a data item composed of multiple primitive data items
String
A(n)____is an array of characters.
Long integer(double precision)
A(n)____is an integer stored in double the normal number of bit positions.
Pointer
A(n)____is the address of another data item or structure.
floating-point notation
Data represented in _____________ is transmitted accurately between computer equipment from different manufacturers if each computer's CPU represents real numbers by using an IEEE standard notation.
Has 16 digit values (0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F). Is commonly used to represent memory and storage addresses
Describe the characteristics of hexadecimal notation.
Has 8 digit values (0,1,2,3,4,5,6,7). Was commonly used with older IBM mainframe systems
Describe the characteristics of octal notation.
1. Compact - stored values consume little "space" 2. Accurate - any value could be represented and processed without error 3. Easy to manipulate - related processing circuitry would be simple, cheap, and fast 4. Standardized - data represented within one computer device would could be recognized and processed by any other device.
Describe the goals of computer data representation.
a class includes methods in addition to static data
How does a class differ from other data structures?
An array is stored in contiguous sequential memory locations, with the first element at the lowest address. A linked list is stored in memory as an unordered and noncontiguous set of list elements, each consisting of a data value and a pointer to the next data list element. Arrays are more compact and easier to read or write than linked lists. Linked lists are easier to update than arrays. Any data item that is of fixed length and seldom changes value (e.g., a customer name field) is best stored in an array. Data items that are of variable length, large size, and which have frequent value changes (e.g., a process queue) are best stored as a linked list.
How is an array stored in main memory? How is a linked list stored in main memory? What are their comparative advantages and disadvantages? Give an example of data that would be best stored as an array. Give an example of data that would be best stored as a linked list?
1. Allocate a new storage location at the end of the list. 2. For each element past the insertion point, copy its value to the next storage location, starting with the last element and working backward to the insertion point. 3. Write the new element's value in the storage location at the insertion point.
How is an element added to a single linked list?
integer, floating point
In a CPU, _______ arithmetic generally is easier to implement than __________ arithmetic because of a simpler data coding scheme and data manipulation circuitry
Radix point
In a positional numbering system, the_____ separates digits representing whole number quantities from digits representing fractional quantity.
Extended Binary Coded Decimal Interchange Code (EBCDIC)
In older IBM mainframe computers, characters were encoded according to the _____ coding scheme.
Floating Memory Model
In the __________, memory addresses consist of a single integer.
Numeric Range
Increasing a numeric representation format's size (number of bits) increases the_____ of values that can be represented.
ISO, Latin-1
The __________ has defined a character-coding table called __________, which combines the ASCII-7 coding table with an additional 128 Western European multinational characters.
low-order bit or lease significant
The ____________ is the bit of lowest magnitude in a byte or bit string.
collating sequence
The ordering of characters in a coding table is called a(n) __________
Underflow or truncation
The result of adding, subtracting, or multiplying two integers might result in overflow but never
Unicode
Unlike ASCII and EBCDIC, ______ is a 16- bit or 32- bit character coding table.
The advantage is that they can be traversed in either direction with equal efficiency. The disadvantages are that more pointers must be updated each time an element is inserted into or deleted from the list.
What are the advantages/disadvantages of a doubly linked list?
1010, 12, A
What are the binary, octal, and hexadecimal representations of the decimal number 10?
a data structure in which each list element contains a pointer to the next list element
What are the characteristics of a single linked list?
ASCII is an old standard limited to american english, it represents uppercase and lowercase letters and digit 0-9. it is also 7 bit coding format. Unicode is new standard with advanced character coding table. it incorporates ASCII as a subset. it uses 32-bit code.
What are the differences between ASCII and Unicode
Insufficient range: uses 7-bit code, 95 printable characters. English based. Latin-1
What are the limitations of ASCII?
A, B, C etc. used to represent characters with integer values via a coding table
What is a character?
is grouping of primitive data items. Arrays, records and linked lists are commonly used data structures.
What is a data structure? list several types of common data structures
A sequence of records on secondary storage; the common Organization schemes for files are sequential and indexed.
What is a file?
is a set or related data values.
What is a list?
the programs in a class
What is a method?
can have both whole and fractional parts
What is a real number?
is an integer that can value a positive or negative value (e.g., +1234 or ‒1234)
What is a signed integer?
A sequence of characters forming a meaningful word, phrase, or other useful group.
What is a string?
an Address represents a specific storage device. a pointer is a data item containing an address. pointers and memory addresses are used to tie together parts of a data structures such as linked list or indexed file.
What is an address? what is a pointer? what purpose are they used for?
It's a data type having two values true or false.
What is boolean data?
mathematical system of manipulating and combining true and false values
What is boolean logic?
Excess notation can be used to represent signed integers. Always uses fixed number of bits with leftmost representing the sign. Twos complement notation encodes positve values as ordinary binary numbers and negative values as the complement of the corresponding positive value plus 1. a notation method represents specific choices in accuracy, numeric range, size and ease of manipulation.
What is excess notation? What is twos complement notation? Why are they needed? In other words, why can't integer values be represented by ordinary binary numbers?
twos complement value is (-2^15 -1) -32768 to 32767. excess notation value is -32768 to 32767. unsigned binary value is (2^16) 0 to 65535.
What is the numeric range of a 16-bit twos complement value? A 16-bit excess notation value? A 16-bit unsigned binary value?
is a single-byte encoding that can represent the first 256 Unicode characters. encode ASCII.
What is the purpose of Latin-1?
entirely new idea in setting up binary codes for text or script characters the interchange, processing, and display of the written texts of the diverse languages of the modern world
What is the purpose of Unicode?
Integers, real, character, boolean, memory address.
What primitive data types can normally be represented and processed by a CPU?
Real numbers consist of both fractional values as well as whole numbers. They also have floating point notation is considerably more complex than twos complement notation. The more greater the complexity, requires more processing circuitry. Computational circuits for real numbers generally have at least 2X more components than for integers
Why are real numbers more difficult to represent and process than integers?
The computer can only read numeric values, so the letter in turn are converted into some character coding scheme such as ASCII, EBCDIC, or Unicode. That's why "A" and "a" will always be false.
Why doesn't a CPU evaluate the expression 'A' & 'a' as true?
because they can be processed with two-state electrical devices that are constructed easily and inexpensively.
Why is binary data representation and signaling the preferred method of computer hardware implementation?
The reason a programmer uses 128 floating point instead of 64 is due to precision. The large format increases the range of the value. Running data in large format can require more complex execution of instruction which as a result could slow down the execution.
Why might a programmer choose to represent a data item in IEEE binary128 floating-point format instead of IEEE binary64 floating-point format? What additional costs might be incurred at runtime (when the application program executes) as a result of using the 128-bit instead of the 64-bit format?
Number of different digit values ex. Decimal number is base 10 and binary is base 2
base