1. Fixed point binary numbers

2. 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.

3. 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 2.333  This becomes more of a challenge

4. 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 68.25  First step is to do the whole number conversion  Then do the fraction side. 1286432168421.1/21/41/81/16 01000100.0100 NOTE You will only ever be asked to convert up to 4 decimal place

5. 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 0.11/20.5 0.011/40.25 0.0011/80.125 0.00011/160.0625 0.000011/320.03125

6. 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

7. Time to try Convert the following to fixed point binary  2.75  3.625  13.375  26.1875  23.5625  6.875  21.3125 Convert the following, assuming 4 bits after the point:  01011000  0110010  11001100  11110110  11010100