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47 CHAPTER 7 - LOGIC There are a number of operations which work on individual bits of a byte or word. Before we start working on them, it is necessary for you to learn the Intel method of numbering bits. Intel starts with the low order bit, which is #0, and numbers to the left. If you look at a byte: 7 6 5 4 3 2 1 0 that will be the ordering. If you look at a word: 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 that is the ordering. The overwhelming advantage of this is that if you extend a number, the numbering system stays the same. That means that if you take the number 45 : 7 6 5 4 3 2 1 0 0 0 1 0 1 1 0 1 (45d) and sign extend it: 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 each of the bits keeps its previous numbering. The same is true for negative numbers. Here's -73: 7 6 5 4 3 2 1 0 1 0 1 1 0 1 1 1 (-73d) 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 (-73d) In addition, the bit-position number denotes the power of 2 that it represents. Bit 7 = 2 ** 7 = 128, bit 5 = 2 ** 5 = 32, bit 0 = 2 ** 0 = 1. {1}. Whenever a bit is mentioned by number, e.g. bit 5, this is what is being talked about. AND We will use AND as the prototype. There are five different ways you can AND two numbers: ____________________ 1 I'm using the Fortran convention for showing exponents. That is, 2 ** 7 is 2 to the 7th, 3 ** 19 is 3 to the 19th. ______________________ The PC Assembler Tutor - Copyright (C) 1989 Chuck Nelson The PC Assembler Tutor 48 ______________________ 1. AND two register 2. AND a register with a variable 3 AND a variable with a register 4. AND a register with a constant 5. AND a variable with a constant That is: variable1 db ? variable2 dw ? and cl, dh and al, variable1 and variable2, si and dl, 0C2h and variable1, 01001011b You will notice that this time the constants are expressed in hex and binary. These are the only two reasonable alternatives. These instructions work bit by bit, and hex and binary are the only two ways of displaying a number bitwise (bit by bit). Of course, with hex you must still convert a hex digit into four binary digits. The table of bitwise actions for AND is: 1 1 -> 1 1 0 -> 0 0 1 -> 0 0 0 -> 0 That is, a bit in the result will be set if and only if that bit is set in both the source and the destination. What is this used for? Several things. First, if you AND a register with itself, you can check for zero. and cx, cx If any bit is set, then there will be a bit set in the result and the zero flag will be cleared. If no bit is set, there will be no bit set in the result, and the zero flag will be set. No bit will be altered, and CX will be unchanged. This is the standard way of checking for zero. You can't AND a variable that way: and variable1, variable1 is an illegal instruction. But you can AND it with a constant with all the bits set: and variable1, 11111111b If the bit is set in variable1, then it will be set in the result. If it is not set in variable1, then it won't be set in the result. This also sets the zero flag without changing the variable. AND is also used in masks, which will be covered at the end of the chapter. Chapter 7 - Logic 49 _________________ Finally, there is a variant of AND called TEST. TEST does exactly the same thing as AND but throws away the results when it is done. It does not change the destination. This means that it can check for specific things without altering the data. It has the same possibilities as AND: variable1 db ? variable2 dw ? test cl, dh test al, variable1 test variable2, si test dl, 0C2h test variable1, 01001011b will set the flags exactly the same as the similar AND instructions but will not change the destination. We need a concrete example, and for that we'll turn to your video card. In text mode, your screen is 80 X 25. That is 2000 cells. Each cell has a character byte and an attribute byte. The character byte has the actual ascii number of the character. The attribute byte says what color the character is, what color the background is, whether the character is high or low intensity and whether it blinks. An attribute byte looks like this: 7 6 5 4 3 2 1 0 X R G B I R G B Bits 0,1 and 2 are the foreground (character) color. 0 is blue, 1 is green, and 2 is red. Bits 4, 5, and 6 are the background color. 4 is blue, 5 is green, and 6 is red. Bit 3 is high intensity, and bit 7 is blinking. If the bit is set (1) that particular component is activated, if the bit is cleared (0), that component is deactivated. The first thing to notice is how much memory we have saved by putting all this information together. It would have been possible to use a byte for each one of these characteristics, but that would have required 8 X 2000 bytes = 16000 bytes. If you add the 2000 bytes for the characters themselves, that would be 18000 bytes. As it is, we get away with 4000 bytes, a savings of over 75%. Since there are four different screens (pages) on a color card, that is 18000 X 4 = 72000 bytes compared to 4000 X 4 = 16000. That is a huge savings. We don't have the tools to access these bytes yet, but let's pretend that we have moved an attribute byte into dl. We can find out if any particular bit is set. TEST dl with a specific bit pattern. If the zero flag is cleared, the result is not zero so the bit was on. If the zero flag is set, the result is zero so that bit was off test dl, 10000000b ; is it blinking? test dl, 00010000b ; is there blue in the background? test dl, 00000100b ; is there red in the foreground? The PC Assembler Tutor 50 ______________________ If we look at the zero flag, this will tell us if that component is on. It won't tell us if the background is blue, because maybe the green or the red is on too. Remember, test alters neither the source nor the destination. Its purpose is to set the flags, and the results go into the Great Bit Bucket in the Sky. OR The table for OR is: 1 1 -> 1 1 0 -> 1 0 1 -> 1 0 0 -> 0 If either the source or the destination bit is set, then the result bit is set. If both are zero then the result is zero. OR is used to turn on a specific bit. or dl, 10000000b ; turn on blinking or dl, 00000001b ; turn on blue foreground After this operation, those bits will be on whether or not they were on before. It changes none of the bits where there is a 0. They stay the same as before. XOR The table for XOR is: 1 1 -> 0 1 0 -> 1 0 1 -> 1 0 0 -> 0 That is, if both are on or if both are off, then the result is zero. If only one bit is on, then the result is 1. This is used to toggle a bit off and on. xor dl, 10000000b ; toggle blinking xor dl, 00000001b ; toggle blue foreground Where there is a 1, it will reverse the setting. Where there is a 0, the setting will stay the same. This leads to one of the favorite pieces of code for programmers. xor ax, ax zeros the ax register. There are three ways to zero the ax register: mov ax, 0 sub ax, ax xor ax, ax Chapter 7 - Logic 51 _________________ The first one is very clear, but slightly slower. For the second one, if you subtract a number from itself, you always get zero. This is slightly faster and fairly clear.{2} For the third one, any bit that is 1 will become 0, and and bit that is 0 will stay 0. It zeros the register as a side effect of the XOR instruction. You'll never guess which one many programmers prefer. That's right, XOR. Many programmers prefer the third because it helps make the code more obsure and unreadable. That gives a certain aura of technical complexity to the code. NEG and NOT NOT is a logical operation and NEG is an arithmetical operation. We'll do both here so you can see the difference. NOT toggles the value of each individual bit: 1 -> 0 0 -> 1 NEG negates the value of the register or variable (a signed operation). NEG performs (0 - number) so: neg ax neg variable1 are equivalent to (0 - AX) and (0 - variable1) respectively. NEG sets the flags in the same way as (0 - number). ; negvsnot.asm ; compares the operations NEG and NOT ; + + + + + + + + + + + + + + + START CODE BELOW THIS LINE mov ax_byte, 1 ; signed mov bx_byte, 1 ; signed mov cx_byte, 1 ; signed mov si_byte, 3 ; binary mov di_byte, 3 ; binary mov bp_byte, 3 ; binary mov dx, 0 ; not used, so clear lea ax, ax_byte call set_reg_style call show_regs outer_loop: call get_signed ; get number mov bx, ax ; move it to all registers mov cx, ax mov si, ax mov di, ax mov bp, ax not bx ; NOT the second row down ____________________ 2 This is one of the first instructions in the template files. The PC Assembler Tutor 52 ______________________ not di neg cx ; NEG the third row down neg bp call show_regs jmp outer_loop ; + + + + + + + + + + + + + + + END CODE ABOVE THIS LINE This is set up so the left registers are signed and the right registers are binary. The top registers retain the original value, the second registers down will do NOT and the third registers down will do NEG. Put a number in. On the right side, you will see that NOT (in DI) reverses the bit pattern, while on the left, NEG (in CX) negates the number. Do a few more. This is always true. But they seem to be related. In fact, BX will always be 1 too negative. Why? Remember that in the introduction on numbers, when we changed signs, we had: negative of number = one's complement + 1 but the one's complement is exactly NEG. It switches the value of each bit. To get the values in the third row (CX and BP), simply add 1 to the values in the second row (BX and DI). Remember, NOT is a logical operation, NEG is an arithmetic operation. MASKS To explain masks, we'll need some data, and we'll use the attribute byte for the monitor. Here it is again: 7 6 5 4 3 2 1 0 X R G B I R G B Bits 0,1 and 2 are the foreground (character) color. 0 is blue, 1 is green, and 2 is red. Bits 4, 5, and 6 are the background color. 4 is blue, 5 is green, and 6 is red. Bit 3 is high intensity, and bit 7 is blinking. What we want to do is turn certain bits on and off without affecting other bits. What if we want to make the background black without changing anything else? We use and AND mask. and video_byte, 10001111b Bits 0, 1, 2, 3 and 7 will remain unchanged, while bits 4, 5 and 6 will be zeroed. This will make the background black. What if we wanted to make the background blue? This is a two step process. First we make the background black, then set the blue background bit. This involves first the AND mask, then an OR mask. and video_byte, 10001111b or video_byte, 00010000b Chapter 7 - Logic 53 _________________ The first instruction shuts off certain bits without changing others. The second turns on certain bits without effecting others. The binary constant that we are using is called a mask. You may write this constant as a binary or a hex number. You should never write it as a signed or unsigned number (unless you are one of those people who just adores making code unreadable). If you want to turn off certain bits in a piece of data, use an AND mask. The bits that you want left alone should be set to 1, the bits that you want zeroed should be set to 0. Then AND the mask with the data. If you want to turn on certain bits in a piece of data, use an OR mask. The bits that you want left alone should be set to 0. The bits that you want turned on should be set to 1. Then OR the mask with the data. Go back to AND and OR to make sure you believe that this is what will happen. The PC Assembler Tutor 54 ______________________ SUMMARY For AND, TEST, OR, and XOR you can have the following combinations: 1. two register 2. a register with a variable 3 a variable with a register 4. a register with a constant 5. a variable with a constant AND is a bitwise logical operation. 1 1 -> 1 1 0 -> 0 0 1 -> 0 0 0 -> 0 TEST does the same thing as AND except that the result is discarded. It is used for setting the flags without altering the data. OR is a bitwise logical operation. 1 1 -> 1 1 0 -> 1 0 1 -> 1 0 0 -> 0 XOR is a bitwise logical operation. 1 1 -> 0 1 0 -> 1 0 1 -> 1 0 0 -> 0 You can use NOT and NEG with either a register or a variable in memory. NOT is a bitwise logical operation 0 -> 1 1 -> 0 NEG is an arithmetic operation. NUMBER -> - NUMBER. It gives the negative of a signed number. MASKS If you want to turn off certain bits of a piece of data, use an AND mask. The bits that you want left alone should be set to 1, the bits that you want zeroed should be set to 0. Then Chapter 7 - Logic 55 _________________ AND the mask with the data. If you want to turn on certain bits of a piece of data, use an OR mask. The bits that you want left alone should be set to 0. The bits that you want turned on should be set to 1. Then OR the mask with the data.