Weak Input Makes an Analog Middle - Electronic Circuits XI: Transistor Switching and Device Regions Step by Step

Active region is not a valid digital output state. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

A weak input produces only a half-ampere of base drive

The input is 3 V, so after the 1 V drop the base current is 1/2 A.

I_B={3\ \text{V} - 1\ \text{V}\over 4\ \Omega}={1\over 2}\ \text{A}

Active region is not a valid digital output claim

The active-region collector current is 3/2 A, leaving the output at 6 V; the state is MIDDLE.

I_C={3\over 2}\ \text{A},\quad V_\text{out}=6\ \text{V}\Rightarrow \text{MIDDLE}