To draw a line on a 320x200 monochrome frame buffer using AVR assembly without decimal numbers, an efficient algorithm is needed. The discussion highlights the use of Bresenham's line algorithm, which avoids floating-point calculations by using integer arithmetic and fixed-point math to determine pixel positions. The frame buffer is managed with 8000 bytes of SRAM, where each byte represents 8 pixels, and the SPI peripheral is utilized for fast data transmission. The program only needs to update the frame buffer when a new line is drawn, and the interrupts handle the display timing. This approach ensures efficient line drawing while maintaining performance on the Atmega1284p.