What does data representation refer to in computing?
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How information is stored within the computer.
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What does data representation refer to in computing?
How information is stored within the computer.
What are the different methods for storing data mentioned in the text?
Integers, floating-point values, and characters.
What is the binary representation of numbers?
The computer represents numbers in binary (1's and 0's).
What is the range of values that can be represented by a byte (8-bits) in unsigned format?
0 to 255 (inclusive).
What is the range of values that can be represented by a byte (8-bits) in signed format?
-128 to +127 (inclusive).
What is the number of different values a word (16-bits) can represent?
65,536 different values.
What is the number of different values a double-word (32-bits) can represent?
4,294,967,296 different numbers.
What must be used if the range of a data type is not large enough to handle intended values?
A larger size must be used.
What is the significance of the prefix '0x' in a number?
It indicates that the number is in hexadecimal format.
What is the range of values for a signed double-word (32-bits)?
-2,147,483,648 to +2,147,483,647
What is the unsigned range for a byte (8-bits)?
0 to 255
What is the signed range for a word (16-bits)?
-32,768 to +32,767
What encoding process is used for representing signed values?
Two's complement
What is the unsigned range for a double-word (32-bits)?
0 to 4,294,967,295
What is the signed range for a quadword?
-(2^63) to 2^63 - 1
What is the size of a byte in bits?
8 bits
What is the size of a word in bits?
16 bits
What is the size of a double quadword in bits?
128 bits
What is the unsigned range for a double quadword?
0 to 2^128 - 1
What is the range of unsigned values compared to signed values?
Unsigned values have a positive only range, while signed values can represent both positive and negative numbers, leading to overlap in the positive range.
What is the two's complement representation used for?
It is used to represent negative values in binary.
What are the steps to find the two's complement of a number?
What is the two's complement representation of -9 in byte size?
F7 (in hex).
What is the two's complement representation of -12 in byte size?
F4 (in hex).
Why can confusion arise when examining variables in memory?
Because of the overlap between unsigned and signed values in the positive range, which can lead to misinterpretation of the data types.
What is the two's complement representation of -18 in 16-bits?
1111111111101110 (hex: 0xFFEE)
What is the two's complement representation of -40 in 16-bits?
1111111111011000 (hex: 0xFFD8)
What is the result of adding 241 and -15 in unsigned representation?
248 (0xF8)
What is the result of adding 241 and -15 in signed representation?
-8 (0xF8)
What is the significance of the value 0xF8 in ASCII?
It represents the degree symbol (°).
Why is it important to define sizes and types of data in operations?
To ensure correct interpretation of the final value being represented.
What floating-point standard is primarily discussed in the document?
IEEE 754 32-bit floating-point standard.
What is the IEEE 754 32-bit floating-point standard used for?
It is used for representing floating-point values in computers.
What does the sign bit 's' represent in the IEEE 754 format?
0 indicates positive and 1 indicates negative.
How is the value N calculated in the IEEE 754 representation?
N = (-1)^s x 1.F x 2^(E-127).
What is the first step in representing floating-point values?
Convert the floating-point value into binary.
What does normalized scientific notation in binary require?
A single, non-zero leading digit to the left of the decimal point.
What is the bias used in the IEEE 754 32-bit floating-point standard?
How is the biased exponent calculated?
It is the exponent from the normalized scientific notation plus the bias.
What is stored in the fraction portion of the IEEE 754 representation?
The numbers after the leading 1, left-justified.
What is the first step in finding the IEEE 754 32-bit representation for a negative number?
Determine the sign, which is 1 for negative numbers.
How is the binary representation of -7.75 expressed in normalized scientific notation?
1.1111 x 2^2
What is the biased exponent for -7.75 in IEEE 754 representation?
129 (computed as 2^10 + 127).
What is the final hexadecimal result for the IEEE 754 representation of -7.75?
C0F80000
What is the binary representation of -0.125 in normalized scientific notation?
1.0 x 2^-3
What is the biased exponent for -0.125 in IEEE 754 representation?
124 (computed as -3 + 127).
What is the sign bit for negative numbers in IEEE 754 representation?
1
How do you convert the biased exponent to binary in IEEE 754 representation?
Convert the biased exponent value to binary format.
How is the hexadecimal representation of the binary number 10111110000000000000000000000000 obtained?
By splitting the binary into groups of 4 and converting each group to hex, resulting in BE00 0000.
What is the decimal value of the IEEE 754 32-bit floating-point representation 41440000?
The decimal value is +12.25.
What is the bias used in the IEEE 754 64-bit floating-point representation?
The bias is ±1023.
What does NaN stand for in floating-point representation?
Not a Number.
What happens when a value does not conform to the IEEE 754 standard?
It is referred to as NaN (Not a Number) and cannot be used as a floating-point value.
What is symbolic data in computing?
Symbolic data refers to non-numeric data such as messages or symbols, like 'Hello World'.
What is a character in computer terms?
A character is a unit of information that corresponds to a symbol, such as a letter, digit, or punctuation mark.
What does ASCII stand for?
American Standard Code for Information Interchange.
How are characters represented in a computer?
Characters are represented by assigning numeric values to each symbol or character using ASCII.
What is the numeric value assigned to the letter 'A' in ASCII?
65 (decimal) or 0x41 (hexadecimal).
What is the difference between characters and integers in computing?
Characters can be displayed but not used for calculations, while integers can be used for calculations but not displayed without changing representation.
How much space is typically allocated for storing a character?
A character is typically stored in a byte (8 bits) of space.
What is an example of a control character?
Examples include carriage return or tab.
What is the purpose of the Unicode Standard?
To provide a unique number for every character, regardless of platform, device, application, or language.
What are the common encoding schemes provided by Unicode?
UTF-8, UTF-16, UTF-32, etc.
How does UTF-8 represent ASCII English text?
It looks exactly the same in UTF-8 as it did in ASCII, with additional bytes used for other characters as needed.
What is a string in computer science?
A series of ASCII characters, typically terminated with a NULL.
What is the purpose of the NULL character in a string?
To mark the end of a string.
How is the string 'Hello' represented in ASCII values?
H: 72, e: 101, l: 108, l: 108, o: 111, NULL: 0.
What is the difference between the string '19653' and the integer 19,653?
The string '19653' uses 6 bytes, while the integer 19,653 can be stored in a single word which is 2 bytes.
