Holding the base resistor fixed turns input-minus-drop voltage into a visible current scan. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
At the drop, the base has zero drive
Input 1 V minus the stated 1 V base-emitter drop leaves 0 V on the base resistor. With 4 ohm fixed, the base current is 0 A.
1V−1V=0V,IB=0A
Two volts of excess gives one half ampere
Input 3 V minus the stated 1 V base-emitter drop leaves 2 V on the base resistor. With 4 ohm fixed, the base current is 1/2 A.
3V−1V=2V,IB=21A
Four volts of excess gives one ampere
Input 5 V minus the stated 1 V base-emitter drop leaves 4 V on the base resistor. With 4 ohm fixed, the base current is 1 A.