Creating a +5V/-4V Clock with a PIC Micro
Another option to throw into the mix, a simple comparator. In order to do it this way you would need a comparator with a push-pull output that can operate from a supply of at least \$5V - (-4V) = 9V\$. I've had a quick look and they do indeed exist, for example TLV7211. That one runs up to \$15V\$ and the SMD package is not much bigger than a surface mount transistor.

You would wire it up as follows:







simulate this circuit &ndash; Schematic created using CircuitLab

While the comparator is not actually specifically rated to run from a split supply, the great thing is it doesn't make a difference in this situation. As far as the comparator is concerned it is operating from a 9V supply. By shifting its ground pin down to -4V, the output will be either -4V and 5V depending on whether the input voltage is higher or lower than the reference voltage.

For the reference voltage, we need it to sit at about 2.5V, or half the input logic level. For the reference divider, you can either connect it between the two supplies as shown, or you can connect R2 to GND instead and make R1 and R2 equal in value.