Data types

Created from P.M.T and Ada Comp. Sci. notes

What number base is binary?

Base 2

What number base is denary?

Base 10

What number base is hexadecimal?

Base 16

Why is hexadecimal often shown to humans insted of binary?

• It is easier to read and interpret…

• … and uses less characters…

• … so is less likely to be written or read incorrectly

Most significant bit (MSB) of a binary number

Bit that is furthest to the left

Least significant bit (LSB) of a binary number

Bit that is furthest to the right

Bit

A single binary digit

Byte

8 bits

Nybble

4 bits; half a byte

Two methods of representing negative numbers in binary

• Sign and magnitude

• Two’s complement

How does sign and magnitude represent numbers?

• MSB is a sign bit - 0 means positive, 1 means negative. This is equivelent to adding a + or - in front of the number

• The rest of the bits show the magnitude (size) of the number

• Example: 01100 →+(8+4)→ 12, and 11100→ -(8+4)→ -12

How does sign and magnitude represent numbers?

• Makes the MSB negative (e.g. in 8 bit number MSB is usually 128, bit in ___ it is -128)

• Rest of the bits are normal

• Example, 01100→(8+4)→12, 10100→(-16+4)→ -12

How do you turn a positive number to its negative equivelent in two’s complement?

• Flip all the bits and add one

• Example: 24=011000, flip bits→100111, add one→101000=-24

How to turn a negative number to its positive equivelent in two’s complement

• Subtract one and flip all the bits

• Flip all the bits and add one

• Example: -19=101101, subtract one→101100, flip bits→010011=19

Advantage of two’s complement over sign and magnitude

It is not easily possible to carry out calculations using sign and magnitude whereas they will work with two’s complement.

Disadvantage of sign and magnitude

• It is not easily possible to carry out calculations using negative numbers in sign and magnitude

• As such it is rarely used in modern systems

You have a fixed number of bits to store a real binary number. Describe the trade-off between accuracy and range when deciding how many bits to use for the mantissa and exponent.

• The larger the mantissa the more accurate the number

• The larger the exponent the greater the range of numbers that can be stored

What does the start of a normalised floating point number start with

• 01 for positive numbers

• 10 for negative numbers

What us a character set?

The characters a computer uses / understands

How is a character set used to represent text in a computer?

• Each character is assigned a unique character code

• Each letter is converted to its character code (which is a binary number)

What would happen if computers were to use different character sets when communicating?

• Characters from a computer using one characterset will be interpreted as different characters by a computer using another character set.

• As such text will be incomprehensible.

Explain how computers are able to represent text.

• Computers use a character set to map binary values to characters

• Each character is represented by a unique value called a bit pattern

Similarities between ASCII and UNICODE

• Both are character sets

• The first 8 bits of UNICODE are the same as ASCII

Disadvantages of ASCII

• Has a very limited number of characters so is not suitable for multilingual text

Advantages of UNICODE over ASCII

• Can represent more characters

• Can represent foreign alphabets

• Can represent emojis and symbols

Disadvantages of UNICODE

• Can take up more storage space