The Radio Push Button function is sometimes desired, where pushing one momentary button of several gives a latched output representing that button, simultaneously cancelling the latched output from the previously pressed button.
Of course a microcontroller can be programmed to perform this function if you have the programming knowledge and a chip programmer, but if not, here is a discrete solution.
Unlike many non-μC circuits that require a clock pulse or RC delay circuits to properly perform this function, the circuit below uses only two commonly available CMOS digital ICs that can operate from 3V to 15V (18V max.) with no clock or passive parts, other than the push buttons and filter cap.
The circuit can be left connected to the power supply, since it draws only the leakage current of the CMOS ICs in the static state (a few tens of microamps max.), allowing the last PB state to be retained indefinitely. Alternately a lithium coin cell could be used to retain the state if the power must be removed.
When the CD4532 Priority Encoder detects a push button input (logic high) it generates a 3-bit binary output word (O0-O2) representing the PB location (I0-I7) of the input. This binary word is decoded by the CD4514 1-of-16 decoder latch to give a high at the corresponding (O0-O7) output (O8 through O15 are unused in this configuration). The priority encoder also generates a pulse (GS) when it detects a PB input, which is used to latch the decoded PB state of the 1-of-16 decoder so the corresponding output remains high when the PB is released.
The circuit can operate with 2 to 8 buttons, as required by the application.
It is shown with 4 buttons but can be readily expanded to 8 by adding push buttons to the unused inputs (I4-I7).
The Multisim-EWB simulation output is shown after PB  was momentarily pushed (Out_3 indicator is red, indicating a logic high) .
To get up to 16 PB inputs, two CD4532s can be cascaded, as shown in this data sheet (Figure 15), to handle 8 more PB inputs, with the addition of three 2-input OR gates (one CD4071 chip) to give a 4-bit priority output. These 4 bits are connected to the corresponding data inputs (A0-A3) of the CD4514, thus utilizing all 16 of its outputs.
The GS signals from the two CD4532s are also OR'd together, using the last CD4071 gate, to generate the EL latch signal for the CD4514
The circuit is shown using SPDT push buttons but SPST buttons can be used if 1k-50kΩ pull-down resistors are added from each PB output to ground.
If you need more output current then the few milliamps the 4514 can supply (varies with supply voltage), you can add an appropriate transistor buffer (either BJT or MOSFET) to each output.
One minor drawback of this circuit is that the CD4514 only comes in a large 24-pin package. I am not aware of any physically smaller single device that will perform its combined function of decoder and latch without additional circuitry.
Radio Push Button Micropower Circuit Using Two Common ICs
Two common ICs generate the Radio PB Function for up to 8 PBs, (16 PBs with 2 additional chips).