BBS: Inland Empire Archive Date: 07-31-92 (09:12) Number: 171 From: JEAN CREPEAU Refer#: NONE To: BRYAN HOOVER Recvd: NO Subj: Colr Attrbt (And 15) Conf: (2) Quik_Bas

In a message to ALL, BRYAN HOOVER wrote: BH=> Can anyone explain how works the formula, ForColr% = Atribute%AND15 ? What's happening with theANDoperator and the number 15? TheANDoperator is a logical operator, likeORand XOR. To understand how it works, you must know what is a binary number and how to convert a decimal (normal) number into binary or vice-versa. A binary number is a set of binary digits (bits). It's exactly like a normal number which use 10 different digits. In binary, you can only use 2 differents digits: 0 and 1. These two symbols represent an electric state: 0V and 5V. You computer use binary numbers 99.9% of the time. Decimal numbers are too complicated. To convert a decimal number into binary, you divide that number by 2. You keep the rest. You divide the result of the division by 2 again and keep the rest. You continue until you get 0. For instance, suppose you want to convert 15: 15/2 = 7 rest 1 7/2 = 3 rest 1 3/2 = 1 rest 1 1/2 = 0 rest 1 The binary number is 1111. 15=1111b! The last rest you get becomes the first digit in the binary sequence... my example wasn't very good! Try 69. 69/2 = 34 rest 1 34/2 = 17 rest 0 17/2 = 8 rest 1 8/2 = 4 rest 0 4/2 = 2 rest 0 2/2 = 1 rest 0 1/1 = 0 rest 1 Then, 69=1000101b. It's easy isn't it? Now to convert you binary number into a decimal number you do the opposite of what you did: you setup an accumulator in your mind. 1. You multiply this accumulator by 2 2. You add the value of the next digit in the sequence 3. You repeat for any extra bit Ex: 110011b=? Acc. Acc*2 Bit Acc*2+Bit 0 0 1 1 1 2 1 3 3 6 0 6 6 12 0 12 12 24 1 25 25 50 1 51 Then, 110011b is 51! The bits are generally numbered. The rightmost one being 0, the preceding one being 1, etc... If you write the mathematic equation the algorithm above, you easily see that number= bit#0 + bit#1*2 + bit#2*2*2 + bit#3*2*2*2 + bit#4*2*2*2*2 + etc... = b0 + b1*2 + b2*4 + b3*8 + b4*16 + etc... A BYTE or character is a binary number of 8 bits. It can take the values 00000000b to 11111111b (0 to 255). A WORD (orINTEGERin QBasic) is a binary number of 16 bits (0 to 65535). A DWORD (or LONG) is 32 bits wide. When you do a logical AND,ORor XOR, you perform bit-by-bit operation with the following truth table: x yANDORXOR0 0 0 0 0 0 1 0 1 1 1 0 0 1 1 1 1 1 1 0 Note that: 1. xAND0 = 0, whatever is x 2. xAND1 = x 3. xANDx = x 4. xOR0 = x 5. xOR1 = 1 6. xORx = x 7. xXOR0 = x 8. xXOR1 = complement of x (0 becomes 1 and 1 becomes 0) 9. xXORx = 0 Often, the information is compressed into memory... 8 bits are not always necessary to store a number. For instance if you want to store a color 0 to 15, you only need 4 bits. Why use 8 bits? you would loose the other 4 bits, unless you want to store 256 different numbers (0 to 255) instead of 16. What we usually do is that we allocate functions to specific bits. For instance, in a graphic card, the attribute BYTE read with PEEK(adress) counts 8 bits: b0 to b3: Foreground (4 bits = 16 different colors 0000-1111) b4 to b6: Background (3 bits = 8 colors 000-111) b7: Blink (1 bit = 0 or 1) If you want to read only the foreground for instance, you must have a way to'ignore' bits b4 to b6. This is done by law #1:b7 b6 b5 b4 b3 b2 b1 b0 AttrAND0 0 0 0 1 1 1 1 15 -- -- -- -- -- -- -- -- ---- 0 0 0 0 b3 b2 b1 b0 FG If you want the background, b7 b6 b5 b4 b3 b2 b1 b0 AttrAND0 1 1 1 0 0 0 0 112 -- -- -- -- -- -- -- -- ---- 0 b6 b5 b4 0 0 0 0 BG*16 Then (AttrAND112)/16 will give you the background color 0-7.ORis use if you want to set some bits andXORwhen you want to invert some bits. Hope this will help you to understand... Binary is not that easy to understand when you never heard about it... I know. Jean --- * Origin: INTERACESS Montreal (QC) Canada (514) 528-1415 (1:167/280)

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