Data Representation (Cambridge (CIE) A Level Computer Science): Flashcards
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- FrontBinary Prefixes
Define binary prefix.
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Define binary prefix.
A binary prefix is a unit prefix used to indicate multiples of bytes in binary.
What is the standard unit used for measuring data storage?
The standard unit used for measuring data storage is the byte.
How many bytes are there in 1 kibibyte (1 KiB)?
1 kibibyte (1 KiB) is 1024 bytes.
How many bytes are there in 1 kilobyte (1 KB)?
1 kilobyte (1 KB) is 1000 bytes.
True or False?
1 gigabyte (1 GB) and 1 gibibyte (1 GiB) contain the same number of bytes.
False.
1 gigabyte (1 GB) is 1,000,000,000 bytes, while 1 gibibyte (1 GiB) is 1,073,741,824 bytes.
Computers use the (base 2) number system, so denary prefixes are technically inaccurate when describing storage.
Computers use the binary (base 2) number system, so denary prefixes are technically inaccurate when describing storage.
Which prefix system should be used when precision is required, for example when describing RAM?
Binary prefixes should be used when precision is required, for example when describing RAM.
Which prefix system is commonly used when a rough estimate is acceptable, such as describing the capacity of a storage device?
Denary prefixes are commonly used when a rough estimate is acceptable, such as describing the capacity of a storage device.
How many bytes can 16 GiB of RAM store?
16 GiB of RAM can store 16 × 2³⁰ bytes, which is 17,179,869,184 bytes.
How many bytes are there in 1 mebibyte (1 MiB)?
1 mebibyte (1 MiB) is 1,048,576 bytes.
Define number base.
A number base is the number of different digits or symbols a number system uses to represent values.
How many digits does the denary number system use, and which base is it?
Denary uses 10 digits (0-9) and is a base-10 number system.
How many digits does the hexadecimal number system use?
Hexadecimal uses 16 digits — the numbers 0-9 and the letters A-F.
One hexadecimal digit can represent bits of binary data.
One hexadecimal digit can represent four bits of binary data.
In any number base, what does each place in a number represent?
Each place represents a power of the base, starting from the right.
What is the denary value of the 8-bit binary number 01101001?
The 8-bit binary number 01101001 is 105 in denary.
What is the binary number 10110111 in hexadecimal?
The binary number 10110111 is B7 in hexadecimal.
What is the denary number 163 in hexadecimal?
The denary number 163 is A3 in hexadecimal.
Define Binary Coded Decimal (BCD).
Binary Coded Decimal is a number system that uses 4-bit codes to represent each denary digit (0-9).
How is the denary number 2500 represented in BCD?
The denary number 2500 is 0010 0101 0000 0000 in BCD.
How is a positive binary number turned into a negative one using one's complement?
The positive binary number is inverted, so every 0 becomes a 1 and every 1 becomes a 0.
True or False?
One's complement has two different representations for zero.
True.
One's complement can have two representations for 0, a positive and a negative one, and this is the main issue with the system.
What two steps turn a positive binary number into a negative one using two's complement?
The positive binary number is inverted, then 1 is added to the rightmost bit.
What range of values can 8-bit two's complement represent?
8-bit two's complement can represent values between +127 (0111 1111) and -128 (1000 0000).
Define binary addition.
Binary addition is summing numbers in base-2, which uses only the digits 0 and 1.
Which digit do you start from when carrying out binary addition?
Binary addition starts from the rightmost digit and moves towards the left.
When does carrying over occur in binary addition?
Carrying over occurs when the sum of a column is greater than 1, passing the excess to the next column on the left.
What is 1001 1010 + 0010 1111 in binary?
1001 1010 + 0010 1111 = 1100 1001.
Define overflow.
Overflow occurs when the sum of two binary numbers exceeds the given number of bits.
What can overflow do to the sign of a result in a signed number representation?
The leftmost bit often serves as the sign bit, and overflow can flip it, incorrectly changing the sign of the result.
True or False?
Overflow generally produces a correct result because the extra bits are stored.
False.
Overflow generally leads to incorrect or unpredictable results, because the extra bits are truncated or wrapped around.
How is binary subtraction carried out?
The number being subtracted is converted into its negative equivalent using two's complement, and the two numbers are then added together.
Using 8-bit two's complement, what is 48 - 12 in binary?
48 - 12 gives 0010 0100, which is 36 in denary.
In two's complement arithmetic the additional bit is ignored, because it does not contribute to the value of the result.
In two's complement arithmetic the additional overflow bit is ignored, because it does not contribute to the value of the result.
Give three uses of Binary Coded Decimal (BCD).
BCD is used in electronic calculators, digital clocks and watches, banking and financial systems, and older or embedded systems.
Why is BCD used in banking and financial systems?
BCD avoids rounding errors when carrying out decimal calculations, which matters especially with money.
Why is BCD well suited to digital clocks and watches?
Time is naturally decimal (for example 12:45), so BCD makes the display logic simpler.
True or False?
BCD is only ever used in modern high-performance systems.
False.
BCD is still found in older or embedded systems, where simple hardware-based decimal output is needed.
Why is hexadecimal preferred over binary when working with large values?
It takes fewer digits to represent a given value in hexadecimal than in binary.
Give two reasons why long binary numbers are harder to work with than hexadecimal.
The more bits a binary number has, the harder it is for a human to read, and the more prone to errors it is when being copied.
Give three places where hexadecimal can be seen.
Hexadecimal is used in MAC addresses, colour codes and URLs.
A typical MAC address consists of 12 hexadecimal digits, which is equivalent to digits in binary.
A typical MAC address consists of 12 hexadecimal digits, which is equivalent to 48 digits in binary.
How many hexadecimal digits make up a typical colour code, and how many binary digits is that?
A typical hexadecimal colour code consists of 6 hexadecimal digits, equivalent to 24 digits in binary.
How is a character outside the standard set included in a URL?
It is converted into a hexadecimal code, which is prefixed with a % sign.
Define character set.
A character set is all the characters and symbols that can be represented by a computer system, each given a unique binary code.
What determines how many characters a character set can represent?
The number of characters is determined by the number of bits used by the character set.
What does it mean to say that a character set is ordered logically?
The codes follow a sequence, so the code for 'B' is one more than the code for 'A'.
How many bits does ASCII use, and how many characters can it represent?
ASCII uses 7 bits, giving 2⁷ unique codes, so it can represent a maximum of 128 characters.
Which bit changes between the uppercase and lowercase version of a letter in ASCII?
The sixth bit changes from 1 to 0 when comparing lowercase and uppercase characters.
True or False?
ASCII can represent characters from all the major world languages.
False.
ASCII only represents the basic characters needed for English, which limits its use for other languages.
How many characters can extended ASCII represent, and why?
Extended ASCII can represent 256 characters, because it uses an 8th bit to give 2⁸ unique codes.
Give two things extended ASCII can represent that standard ASCII cannot.
Extended ASCII adds mathematical operators, more recent symbols such as ©, non-English characters and drawing characters.
Define UNICODE.
UNICODE is a character set created as a solution to the limitations of ASCII, using a minimum of 16 bits so it can represent characters from all the major languages.
As a minimum, how many characters can UNICODE represent?
UNICODE can represent a minimum of 65,536 characters, from 2¹⁶ unique codes.
The first characters in the UNICODE character set are the same as ASCII.
The first 128 characters in the UNICODE character set are the same as ASCII.
Give one benefit of using ASCII rather than UNICODE.
ASCII uses a lot less storage space than UNICODE.
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