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% AND 15
? What's happening with the AND operator and the number 15?
The AND operator is a logical operator, like OR and 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 (or INTEGER in 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, OR or XOR, you perform bit-by-bit
operation with the following truth table:
x y AND OR XOR
0 0 0 0 0
0 1 0 1 1
1 0 0 1 1
1 1 1 1 0
Note that:
1. x AND 0 = 0, whatever is x
2. x AND 1 = x
3. x AND x = x
4. x OR 0 = x
5. x OR 1 = 1
6. x OR x = x
7. x XOR 0 = x
8. x XOR 1 = complement of x (0 becomes 1 and 1 becomes 0)
9. x XOR x = 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
b7 b6 b5 b4 b3 b2 b1 b0 Attr
AND 0 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 Attr
AND 0 1 1 1 0 0 0 0 112
-- -- -- -- -- -- -- -- ----
0 b6 b5 b4 0 0 0 0 BG*16
Then (Attr AND 112)/16 will give you the background color 0-7.
OR is use if you want to set some bits and XOR when 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
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* Origin: INTERACESS Montreal (QC) Canada (514) 528-1415 (1:167/280)
