Understanding Math with the 6502 Microprocessor
In today’s lab, we’ll try to get our hands on the maths and seeing how the screen reflects the output. The code is provided and we’ll try to further experiment with it.
;
; draw-image-subroutine.6502
;
; This is a routine that can place an arbitrary
; rectangular image on to the screen at given
; coordinates.
;
; Chris Tyler 2024-09-17
; Licensed under GPLv2+
;
;
; The subroutine is below starting at the
; label "DRAW:"
;
; Test code for our subroutine
; Moves an image diagonally across the screen
; Zero-page variables
define XPOS $20
define YPOS $21
START:
; Set up the width and height elements of the data structure
LDA #$05
STA $12 ; IMAGE WIDTH
STA $13 ; IMAGE HEIGHT
; Set initial position X=Y=0
LDA #$00
STA XPOS
STA YPOS
; Main loop for diagonal animation
MAINLOOP:
; Set pointer to the image
; Use G_O or G_X as desired
; The syntax #<LABEL returns the low byte of LABEL
; The syntax #>LABEL returns the high byte of LABEL
LDA #<G_O
STA $10
LDA #>G_O
STA $11
; Place the image on the screen
LDA #$10 ; Address in zeropage of the data structure
LDX XPOS ; X position
LDY YPOS ; Y position
JSR DRAW ; Call the subroutine
; Delay to show the image
LDY #$00
LDX #$50
DELAY:
DEY
BNE DELAY
DEX
BNE DELAY
; Set pointer to the blank graphic
LDA #<G_BLANK
STA $10
LDA #>G_BLANK
STA $11
; Draw the blank graphic to clear the old image
LDA #$10 ; LOCATION OF DATA STRUCTURE
LDX XPOS
LDY YPOS
JSR DRAW
; Increment the position
INC XPOS
INC YPOS
; Continue for 29 frames of animation
LDA #28
CMP XPOS
BNE MAINLOOP
; Repeat infinitely
JMP START
; ==========================================
;
; DRAW :: Subroutine to draw an image on
; the bitmapped display
;
; Entry conditions:
; A - location in zero page of:
; a pointer to the image (2 bytes)
; followed by the image width (1 byte)
; followed by the image height (1 byte)
; X - horizontal location to put the image
; Y - vertical location to put the image
;
; Exit conditions:
; All registers are undefined
;
; Zero-page memory locations
define IMGPTR $A0
define IMGPTRH $A1
define IMGWIDTH $A2
define IMGHEIGHT $A3
define SCRPTR $A4
define SCRPTRH $A5
define SCRX $A6
define SCRY $A7
DRAW:
; SAVE THE X AND Y REG VALUES
STY SCRY
STX SCRX
; GET THE DATA STRUCTURE
TAY
LDA $0000,Y
STA IMGPTR
LDA $0001,Y
STA IMGPTRH
LDA $0002,Y
STA IMGWIDTH
LDA $0003,Y
STA IMGHEIGHT
; CALCULATE THE START OF THE IMAGE ON
; SCREEN AND PLACE IN SCRPTRH
;
; THIS IS $0200 (START OF SCREEN) +
; SCRX + SCRY * 32
;
; WE'LL DO THE MULTIPLICATION FIRST
; START BY PLACING SCRY INTO SCRPTR
LDA #$00
STA SCRPTRH
LDA SCRY
STA SCRPTR
; NOW DO 5 LEFT SHIFTS TO MULTIPLY BY 32
LDY #$05 ; NUMBER OF SHIFTS
MULT:
ASL SCRPTR ; PERFORM 16-BIT LEFT SHIFT
ROL SCRPTRH
DEY
BNE MULT
; NOW ADD THE X VALUE
LDA SCRX
CLC
ADC SCRPTR
STA SCRPTR
LDA #$00
ADC SCRPTRH
STA SCRPTRH
; NOW ADD THE SCREEN BASE ADDRESS OF $0200
; SINCE THE LOW BYTE IS $00 WE CAN IGNORE IT
LDA #$02
CLC
ADC SCRPTRH
STA SCRPTRH
; NOTE WE COULD HAVE DONE TWO: INC SCRPTRH
; NOW WE HAVE A POINTER TO THE IMAGE IN MEM
; COPY A ROW OF IMAGE DATA
COPYROW:
LDY #$00
ROWLOOP:
LDA (IMGPTR),Y
STA (SCRPTR),Y
INY
CPY IMGWIDTH
BNE ROWLOOP
; NOW WE NEED TO ADVANCE TO THE NEXT ROW
; ADD IMGWIDTH TO THE IMGPTR
LDA IMGWIDTH
CLC
ADC IMGPTR
STA IMGPTR
LDA #$00
ADC IMGPTRH
STA IMGPTRH
; ADD 32 TO THE SCRPTR
LDA #32
CLC
ADC SCRPTR
STA SCRPTR
LDA #$00
ADC SCRPTRH
STA SCRPTRH
; DECREMENT THE LINE COUNT AND SEE IF WE'RE
; DONE
DEC IMGHEIGHT
BNE COPYROW
RTS
; ==========================================
; 5x5 pixel images
; Image of a blue "O" on black background
G_O:
DCB $00,$0e,$0e,$0e,$00
DCB $0e,$00,$00,$00,$0e
DCB $0e,$00,$00,$00,$0e
DCB $0e,$00,$00,$00,$0e
DCB $00,$0e,$0e,$0e,$00
; Image of a yellow "X" on a black background
G_X:
DCB $07,$00,$00,$00,$07
DCB $00,$07,$00,$07,$00
DCB $00,$00,$07,$00,$00
DCB $00,$07,$00,$07,$00
DCB $07,$00,$00,$00,$07
; Image of a black square
G_BLANK:
DCB $00,$00,$00,$00,$00
DCB $00,$00,$00,$00,$00
DCB $00,$00,$00,$00,$00
DCB $00,$00,$00,$00,$00
DCB $00,$00,$00,$00,$00
I know it’s a lot of code, but see how fun it is. We’re directly controlling the pixels of our screen.
To build intution we’ll try to understand some basics, which personally helped me to understand. So i did bu roughly categorising it into four blocks by which the code will make a lot more sense at first glance.
1. Setup and Initialization
The program starts by defining some zero-page variables:
XPOS
andYPOS
store the current position of the image on the screen.XDIR
andYDIR
store the direction of movement (left/right for X, up/down for Y).
The image data is stored in memory as 5x5 pixel grids:
G_X
is a yellow "X."G_O
is a blue "O."G_BLANK
is a black square (used to erase the image).
2. Main Loop
The
MAINLOOP
is the core of the program. It does the following:Draws the Image:
- Calls the
DRAW
subroutine to place the image at the currentXPOS
andYPOS
.
- Calls the
Delays:
- A simple delay loop (
DELAY
) is used to slow down the animation so it’s visible.
- A simple delay loop (
Erases the Image:
- Draws a blank image (
G_BLANK
) at the current position to clear the old image.
- Draws a blank image (
Updates the Position:
Checks if the image has hit the edge of the screen.
If it has, it reverses the direction (
XDIR
orYDIR
).Updates
XPOS
andYPOS
based on the direction.
3. DRAW Subroutine
The
DRAW
subroutine is responsible for drawing the image on the screen. Here’s how it works:Saves Inputs:
- Stores the
X
andY
positions in zero-page memory.
- Stores the
Calculates Screen Address:
The screen is a 32x32 grid, so each row is 32 bytes apart.
The starting address of the image is calculated as:
Screen Address = $0200 + (YPOS * 32) + XPOS
Copies Image Data:
- The image data is copied row by row from the image pointer (
IMGPTR
) to the screen pointer (SCRPTR
).
- The image data is copied row by row from the image pointer (
Advances to the Next Row:
- After copying a row, the pointers are updated to point to the next row.
Repeats Until Done:
- The process repeats until all rows of the image are drawn.
4. Image Data
The images are defined using
DCB
(Define Constant Byte) directives:Each byte represents a pixel.
For example,
G_X
is a yellow "X" on a black background:DCB $07,$00,$00,$00,$07 DCB $00,$07,$00,$07,$00 DCB $00,$00,$07,$00,$00 DCB $00,$07,$00,$07,$00 DCB $07,$00,$00,$00,$07
Bouncing Graphic
Set the initial position for the graphic
The first task was the have the box start moving diagonally starting from a new starting location.
Old Code
LDA #$00
STA XPOS
STA YPOS
New Code
LDA #$02
STA XPOS
LDA #$05
STA YPOS
Select an X increment that is -1 or +1, and a Y increment that is -1 or +1
Create two new zero-page variables, XINCREMENT
and YINCREMENT
, and set them to 1. This means the image initially moves down-right.
; Zero-page variables
define XINCREMENT $22
define YINCREMENT $23
; Select the increments
LDA #$01
STA XINCREMENT ; start moving right (+1)
LDA #$01
STA YINCREMENT ; start moving down (+1)
Successively move the graphic and make it bounce around the screen
This is how the code flows:
Move the Graphic:
- The graphic’s position is updated every frame by adding
+1
or-1
to its X and Y coordinates. This makes it move right/left or up/down.
- The graphic’s position is updated every frame by adding
Bounce Off the Edges:
When the graphic hits the right or left edge of the screen, its horizontal direction flips (right becomes left, and vice versa).
Similarly, when it hits the top or bottom edge, its vertical direction flips (up becomes down, and vice versa).
Repeat Forever:
- This process loops continuously, creating a smooth bouncing animation.
; setup code
; start of the main loop
; Increment the X position
; ---------------------------
; If XINCREMENT is #$01, we move right by adding 1
; If XINCREMENT is #$FF, we move left by adding -1
LDA XPOS
CLC ; Clear carry before addition
ADC XINCREMENT ; Add XINCREMENT to XPOS
STA XPOS
; Check horizontal boundaries
; ---------------------------
; Check if XPOS == XBOUNDARY (right edge)
LDA XPOS
CMP #XBOUNDARY
BNE CHECK_X_LEFT ; If not equal, jump to check left boundary
; If we hit the right boundary, reverse direction
LDA #$FF
STA XINCREMENT
CHECK_X_LEFT:
; Check if XPOS == 0 (left edge)
LDA XPOS
CMP #0
BNE UPDATE_Y ; If not equal, jump to update Y coordinate
; If we hit the left boundary and direction == left, reverse direction
LDA #$01
STA XINCREMENT
UPDATE_Y:
; Update YPOS using YINCREMENT
; ----------------------------
; If YINCREMENT is #$01, we move down by adding 1
; If YINCREMENT is #$FF, we move up by adding -1
LDA YPOS
CLC ; Clear carry before addition
ADC YINCREMENT ; Add YINCREMENT to YPOS
STA YPOS
; Check vertical boundaries
; ---------------------------
; Check if YPOS == YBOUNDARY (bottom edge)
LDA YPOS
CMP #YBOUNDARY
BNE CHECK_Y_TOP ; If not equal, jump to check the top edge
; If we hit bottom edge, reverse direction
LDA #$FF
STA YINCREMENT
CHECK_Y_TOP:
; Check if YPOS == 0 (top edge)
LDA YPOS
CMP #0 ; If no boundary hit, continue moving
BNE MAINLOOP
; If we hit top edge, reverse direction
LDA #$01
STA YINCREMENT
JMP MAINLOOP ; Return to the main loop
; DRAW subroutine
Challenges
Reflections
Assembly language seems too easy but the process it really tough. What i like about this is after process satisfaction that somehow i did and really i am too afraid in the process but after doing it my undersatnding always shoots up. One thing personally helped me is reading and researchin a lot by which i become curious otherwise it would be very boring for me. For refrence to my code refer to github link.