Section 3 - Data Representation - Part 1 Flashcards
What is a natural number?
A whole number that is used in counting
What is a rational number?
Any value that can be expressed as a ration or fraction
What is an irrational number?
A value that cannot be expressed as a fraction and has an endless series of repeating digits
What is a real number?
A real number is any natural, rational or irrational number. It is the set of all possible real world quantities
What are ordinal numbers?
Numbers that describe the numerical position of objects
What base is decimal?
10, with digits 0 - 9
What base is hexadecimal?
16, with digits 0 - 9 and A - F
What base is binary
2, with digits 0 and 1
How do you convert from binary to hex?
Split the binary number into groups of 4 binary digits and convert each group to their hex equivalent
How do you convert from hex to binary?
Convert each hex digit into the equivalent value with 4 binary digits
How do you convert from hex to decimal?
Multiply the left column by 16 and the right column by 1, then sum the results
How do you convert from decimal to hex?
Convert the decimal number to binary, then the binary into hex
Why is hex used?
- Fewer mistakes will be made when copying the value as it is shorter
- It is easier to remember
What is a bit?
A fundamental unit of information, either a single 1 or 0. They are used to represent the 2 electronic states (on and off)
What is a byte?
A set of 8 bits
What is a nibble?
A set of 4 bits
What is the number of values that can be represented by n bits?
2^n
What is ASCII code?
Previously it was the standard code for representing the characters on the keyboard. It uses 7 bits, forming 128 different bit combinations which is more than enough to cover all the characters on a standard English-Language keyboard
Why can ASCII not be used for arithmetic?
The number character is not the same as the actual number value. For example the ASCII value for 7 is 0110111 which is actually 55 in binary
How many bits are there in ASCII code?
Originally ASCII code used 7 bits, however an 8-bit version was developed to include an additional 128 combinations to represent symbols
What is unicode?
The global standard for multilingual data. There are 16 and 32 bit variations. It is compatible with ASCII because the first 128 codes are the sameW
What is the downside of unicode?
Unicode encodings take more storage space, increasing file size and transmission times
What is error checking?
A variety of systems used to verify that the data they receive is actually the same as the data that was sent
Why do computer systems use error checking?
Bits can change during transmission due to interference
What are parity bits?
An additional bit used to check that the other bits transmitted are likely to be correct. Computers use either odd or even parity
What is majority voting?
A system that requires each bit to be sent 3 times. If a bit value is flipped erroneously during transmission over a noisy line, the recipient computer would use the majority rule and assume that the 2 bits that have not changed were therefore correct.
What are checksums?
A mathematical algorithm that is applied to a packet of data. The data in the block is used to create a checksum value which is transmitted alongside the block. The same algorithm is applied to the block after transmission and if the 2 checksum match then the transmission is considered successful. If they do not match then the block is transmitted again
What are check digits?
An additional digit at the end of a string of other numbers designed to check for mistakes in input or transmission
What check digits do books use?
They have a unique ISBN or EAN. The first 12 digits are the unique item number and the 13th number is the check digit. It can be calculated using the Modulo 10 system
When does an overflow error occur in binary addition?
Where a carry from the most significant bit requires another bit
What is the difference between signed and unsigned binary numbers?
A signed representation can represent both positive and negative numbers, unsigned representation of binary numbers can only represent positive numbers
What is two’s complement?
A representation of a signed binary number
How can you work out the range that can be represented by two’s compliment?
-2^(n-1) to 2(n-1) - 1
How can you convert a negative decimal number to binary?
Work out the positive equivalent of the number, then flip all the bits and add 1
How can you convert a negative binary number to decimal?
Flip all the bits and add 1 before converting the binary number as usual
How can you do subtraction with two’s complement?
By converting the negative number to it’s two’s complement form and adding both numbers, ignoring any carry on
What are fixed point binary numbers used for?
To represent fractions in binary, with a binary point used to separate the whole place values from the fractional part
How can you convert a decimal fraction to fixed point binary?
You use the same technique when converting any number into binary
What are the issues with fixed point binary?
- Some fractions cannot be represented at all due to requiring an infinite number of bits to the right of the point. This will result in truncation and numbers being stored inaccurately
- The range of the fixed point binary number is limited by the fractional part requiring a lot of bits to store. This means storing fixed point binary numbers is extremely resource intensive
