Fixed point binary numbers

Objectives  Draw a distinction between integers and numbers with a fractional part in a computer context.  Describe how an unsigned denary number with a fractional part is represented in fixed-point form in binary.

Numbers  A whole number is called an integer  Integers are great because they can easily be converted to binary  But… it’s generally accepted at some stage fractional numbers will occur  For example  7 divide by 3 will equal  This becomes more of a challenge

Negative numbers!!  Once again we use the magic numbers but this time we are going to add a decimal place and some fractions.  The other side of the decimal place we have to use fractions and half each time Lets have a go at converting  First step is to do the whole number conversion  Then do the fraction side /21/41/81/ NOTE You will only ever be asked to convert up to 4 decimal place

Fraction Conversion  So it’s fairly standard thing to know that  ½ = 0.5  ¼ = 0.25  But a little more difficult after that Binary fractionFractionDecimal Fraction 0.11/ / / / /

Fixed point binary numbers  There are other ways of representing fractional numbers but you don’t need to know about these yet!  The advantage of fixed point is that it is exactly the same as integer arithmetic, making processing faster  The disadvantage is that it has limited range

Time to try Convert the following to fixed point binary  2.75       Convert the following, assuming 4 bits after the point:     