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

Makes binary arithmetic with negative numbers much more simple

Disadvantage of sign and magnitude

• Makes binary arithmetic with negative numbers more complicated

• 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