6.144 MHz = 6144 kHz = 5 * 1228.8 kHz. Most serial ports need a clock at 16 times the baud rate. For 76800 baud, this is 16 * 76.8 kHz = 1228.8 kHz. Lower baud rates (except 110 baud) are 76800 baud divided by a power of two: 38400 baud, 19200 baud, 9600 baud, 4800 baud, 2400 baud, 1200 baud, 600 baud, 300 baud. For 115200 baud (pioneered by the original IBM PC), 115.2 kHz * 16 = 1843.2 kHz = 1.5 * 1228.8 kHz.
Thanks Dave for the wikipedia reference.In a radio project 20 years ago, I had to do a divide-by-a-constant operation where the constant divisor depended on the crystal frequency. I was using a microcontroller that lacked multiply and divide instructions, and programming in assembler. I multiplied by the reciprocal of the divisor by manually implementing shift-and-add operations, one add for each 1 bit in the reciprocal. I chose the exact custom crystal frequency to minimize the number of 1's in the divisor. International Crystal Manufacturing Company still existed then, so I ordered custom crystals from them.
