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First, the software puts all of the devices into Instruction Register mode, which connects all of their instruction registers in series. It then clocks a zero followed by a long string of ones through the chain, which allows it to count the total number of instruction register bits across all of the devices.
All ones is the standard instruction for device bypass, which means that in Data Register mode, each device will introduce only a single bit of delay in the JTAG chain. So the software next puts all of the devices into Data Register mode and once again counts the total number of bits in the chain, which now corresponds to the number of devices in the chain.