Boolean Operations

UMBC CMSC 211

Introduction

Computer hardware often requires that several pieces of information be encoded into a single word or byte. Many programs also pack the information to save memory, disk space or communications time.

Each character to be displayed has an associated attribute byte holding bits to keep track of the red, green, and blue, three more keep keep track of the background color, one bit determines if it is high or low intensity, and one bit to set blinking on or off.
Graphics programming oftens requires turning on or off or small groups of bits representing a single dor or pixel on the screen.
The PC keyboard has several shift keys (two regular, Ctrl, Alt, Num Lock, Insert mode, etc.) The status of each key is recorded as a single bit in the BIOS Data section of memory, and individual bits must be set or interrogated by the BIOS as keys are pressed.
Part of the directory information about each file on the disk s the date and time of last modification. To save space, each of the two is packed into a single word.
Information controlling serial (COM) ports such as Baud rate, parity, and data and stop bits is packed into a single word.
File allocation on disks is controlled by the File Allocation Table (FAT). On floppy disks, each entry in the table is twelve bits long -- one byte and the first four bits of the the next byte or the last four bits of one byte and all of the next byte.

There for bit operations consist of extracting or altering packed information, with either Boolean operatons and shifts.

Boolean Operations

There are four Boolean operations that are the same as in the bitwise logical operators in C: AND, OR, XOR (eXclusive OR), and NOT. These operations can be expressed in the form of truth tables, where false is zero and true is one:

AND Truth Table

A	B	A and B
0	0	0
0	1	0
1	0	0
1	1	1

Examples

        1011 1010
    AND 0000 1111
        0000 1010

        1111 1111
    AND 0000 1111
        0000 1111

OR Truth Table

A	B	A or B
0	0	0
0	1	1
1	0	1
1	1	1

Examples

        1011 1010
    OR  0000 1111
        1011 1010

        1111 1111
    OR  0000 1111
        0000 1111

XOR Truth Table

A	B	A xor B
0	0	0
0	1	1
1	0	1
1	1	0

Examples

        1011 1010
    XOR  0000 1111
        1011 0000

        1111 1111
    OR  0000 1111
        1111 0000

NOT Truth Table

A	not A
0	1
1	0

Examples

   NOT 1011 1010
       0100 0101

   NOT 0000 1111
       1111 0000

Format

These instructions come in the form (No more than one operand is a memory reference):

and/or/xor	reg/mem, reg/mem/constant
not	reg/mem

The functionality is:

and	dest, source	; dest := dest AND source
or	dest, source	; dest := dest OR source
xor	dest, source	; dest := dest XOR source
not	dest	; dest := NOT dest

The not operation is a 1's complement.

The and operation is used to clear bits and the or operation is used to set bits. The xor operation is used to toggle bits to the opposite set. The source is known as the mask for the operation.

AND,OR, XOR set the zero and sign flags according to the result and the overflow and carry flags are cleared.

The most common usage is to AND with a mask and then do a jz to determine if any of the bits corresponding to the mask were a 1. It is so common that they built a special instruction for it:

test	reg/mem, reg/mem/constant

right to left, starting with zero. That means that bit n has the numerical value of 2ⁿ.

An Example

We have already talked about how the keyboard hardware does not know anything about ASCII code, it just knows about scan codes. It is simply a number (using the low seven bits in a byte). The high bit is used to show if the key was pressed (set to 0) or released (set to 1). Then the BIOS (BASIC Input-Output System) has to do its magic. In addition to keeping track of which key was pressed, the BIOS also keeps track of additional information which is stored at memory address 0417h. This is the keyboard status information:

Bit	Mask	Interpretation
7	10000000B	Insert mode on
6	01000000B	Caps lock on
5	00100000B	Num lock on
4	00010000B	Scroll lock on
3	00001000B	Alt key down (either if more than one)
2	00000100B	Ctrl key down (either if more than one)
1	00000010B	Left shift key down
0	00000001B	Right shift key down

If the state is on (Insert mode is set) then the corresponding bit in the keyboard status will be true (1). Forunately for us, the BIOS does all the work to keep the keyboard status up-to-date.

Suppose that we are writing a program where we will do one thing if a certain key is pressed, but do something slightly different if the combination of Alt and a certain key is press. We will want to set a flag based on the Alt key and then proceed with the processing. We could do something like:

.MODEL small

.STACK 100h

ALTKEY EQU 00001000B

.DATA

kbdStatus DB ?

altFlag DB 0 ; Initialized to off

.CODE

example1 PROC

mov ax, @data

mov ds, ax

; ... ; Do something to get the keyboard status

mov ax, kbdStatus

and ax, ALTKEY

jne noAlt

mov bx, 1 ; Set the flag because the Alt key was pressed

mov bx, altFlag

noAlt:

mov al,0

mov ah, 4ch

int 21h

example1 ENDP

END example1

Another Example

The directory information for a disk file constains the date of last modification in a single work in the following format:

year - 1900	bits 9 - 15 (leftmost seven bits)
month	bits 5 - 8 (January is 1)
day	bits 0 - 4 (rightmost five bits)

Now we can do the following:

.MODEL small

.STACK 100h

YEARMASK EQU 1111111000000000B

MONTHMASK EQU 0000000111100000B

DAYMASK EQU 0000000000011111B

.DATA

modDate DW ? ; The year is still in bits 9 - 15

funnyYear DW ? ; The month is still in bits 5 - 8

funnyMonth DW ? ; The day is in bits 0 - 4 and
; all other bits are off

OKDay DW ?

.CODE

example2 PROC

mov ax, @data

mov ds, ax

; ... ; Do something to get the
; modification date

mov ax, modDate

and ax, YEARMASK

mov funnyYear, ax

mov ax, modDate

and ax, MONTHMASK

mov funnyMonth, ax

mov ax, modDate

and ax, DAYMASK

mov ax, OKDay

; At this point, the values
; are not usualable yet

mov al,0

mov ah, 4ch

int 21h

example2 ENDP

END example2

UMBC | CSEE

	.MODEL	small
	.STACK	100h
ALTKEY	EQU	00001000B
	.DATA
kbdStatus	DB	?
altFlag	DB	0	; Initialized to off
	.CODE
example1	PROC
	mov	ax, @data
	mov	ds, ax
;	...		; Do something to get the keyboard status
	mov	ax, kbdStatus
	and	ax, ALTKEY
	jne	noAlt
	mov	bx, 1	; Set the flag because the Alt key was pressed
	mov	bx, altFlag
noAlt:
	mov	al,0
	mov	ah, 4ch
	int	21h
example1	ENDP
	END	example1