167. Instruction bne

Why this step exists

Zero clear records a non-equal result from an earlier operation, so BNE can branch without performing another comparison.

In this step, add exactly this implementation

`emulator/cpu/instructions.py::bne`::

def bne(cpu: CPU, offset: int):
    if not cpu.flags.get_zero_flag():
        cpu.pc = (cpu.pc + offset) & 0xFFFF

The function applies the signed displacement to the already advanced PC and constrains the target to 16 bits.

Invariants: Zero clear takes the branch, including wrapping underflow or overflow; Zero set leaves PC unchanged. Flags, other registers, and memory remain untouched. Misconception: BNE tests Zero, not Negative, and does not perform a comparison or fetch an operand.

Out of scope: BPL/BMI/BVC/BVS are lessons 168-171. Branch opcode imports, handlers, and table entries are deferred to lessons 172-179.