4.5.4 - binary number systems

signed binary

used to represent negative numbers

how do computers subtract

by adding negative numbers

fixed point binary

uses a specified number of bits before and after the binary point

floating point binary

uses a mantissa and an exponent to find where the binary point should go

advantages of floating point

- allows for a representation of a greater range of numbers with a given number of bits

disadvantges of floating point

- complexity

- precision errors (rounding)

- uses more memory

mantissa

significant digits

exponent

the power of 2 applied to the mantissa

rounding error

when decimal numbers cannot be represented exactly in binary

underflow error

when very small numbers are not able to be represented so is approximated as zero

overflow error

when a number is too large to be represented with the available bits

absolute error

the actual difference between the given value and the actual value

relative error

relative error is a measure of uncertainty (absolute error/actual value)

normalisation

removing unnecessary values from the start of a binary number to add them to allow for more at the end

adding binary

0 + 0 = 0

0 + 1 = 1

1 + 1 = 10

1 + 1 + 1 = 11

multiplying binary

same as usual, different addition

how to show number of permutations from a bit (n)

2^n

prefix for binary?

kibi (1024)

prefix for decimal?

kilo (1000)