williams-et-al-1983-apple-ii-computer-graphics

166 APPLE II COMPUTER GRAPHICSThen convert each hex digit to decimal which gives you(8 x 4©96) + (9 x 256) + (1 © x 16) + (1 1 x 1) = 35243.There is a variation on this method which is handy when you are proficientwith hex bytes. When dealing with bytes, recall from Chapter 2 we mentionedthat two hex digits could be used to represent one base 256 digit.Then the address given by $FF3A can be calculated as($FF x 2561) + ($3A x 256°)= (255 x 256) + (58 x 1)= 35243To use this idea efficiently, you must know or be able to quickly calculatethe value of numbers like $3A-a skill that comes with practice.The expanded fo rm method also works when converting binary to decimal,but since binary is base two, you get two to all those powers insteadof sixteen. From right to left in binary, the first position is the ones (2°)place, then the two's (21) place, the four's (22) place, the eight's (23) place,and so on. Therefore, you may write ! 1 1 ©1 ©1 as(1 x 25) + (1 x 24) + (© x 23) + (1 x 22)+ (© x 21) + (1 x 2°)Or even simpler, since it is either one or zero times the place value32 + 16 + 4 + 1= 53This was calculated by adding the place values with ones in them, andignori ng the places containing zeros.Wonderfu l, but you already knew how to convert from binary and hexto decimal. These ideas will help you to become more fam iliar with whatyou are doing, and make you faster and more flexible in your conversions.Conve rting to decimal is fairly straightforward, but unfortunately the sameis not true of converting from decimal to binary or hex.Decimal ta BinaryWhen converting to binary, you can start by fi nding the highest power oftwo which will go into the decimal number-if you can get your hands ona calculator, now would be a good time to do so. Let's take 421 as anexample to convert: 29 (512) is too large to divide by 421, but 28 = 256 (anumber to know in computing), and 256 will divide 421, albeit with aremainder of 165 (42 1-256), so we have a 1 in the 28 place which will beon the left end of our binary number. The next lowest power of two is 128,which divides 165 leaving a remainder of 37. So far our binary number is11 xxxxxxx. Dropping to the next power of two (64) we see that it will notdivide the present remainder (37) so we put a zero in the next place in our