compsci 4.5.4

unsigned integer

integer that is positive, no sign needed

signed integer

integer set as positive or negative through sign

overflow error

number of bits exceeds the maximum number of bits that can be stored.

two’s complement

reverse the whole binary number and then add one to make it negative

binary subtraction

turn number into negative version, then add together

fixed point binary

binary point in the number is fixed on the number line.

disadvantages of fixed point

cannot represent recurring decimals

floating point binary

binary point floats according to exponent

exponent

contains how far the binary point moves

mantissa

contains the actual binary number, and is normalised for accuracy

representation error

fractional part may not always be able to be represented

truncation

discarding bits that cannot be stored; at a loss of accuracy

rounded bits

dropping LSB, but if LSB is one, then add one to whole bit pattern

absolute error

difference between approximate value and original value

advantage of absolute error

allows comparison in order to find out which approximation is better

relative error

absolute error / original value

advantage of relative error

finds percentage the error is off by, finds impact of absolute error.

normalised floating point

floating point number starting with 01 or 10

advantage of normalisation

maximises precision for number in a given number of bits

underflow error

result is too small, and must be rounded