Is it possible to connect a 36 pin 4 digit 7 segment display on an Arduino Uno R3?
Only need 4, or 5 pins; SCK (D13), MOSI (D11), slave select (D10).
Maybe PWM (D9) for brightness.
D12 not used, but is tied up as part of SPI bus.

Connect the Anodes to +5.

Connect the cathodes, with a current limit resistor per cathode, to the outputs of 4 TPIC6C595, or TPIC6B595. 

For the resistor, assume worst case voltage drop of 2V and 20mA current draw:
(5V - 2V)/.02A = 150 phm.

Use a PWM output pin to drive the OE/ pin of the '595s for brightness control.

Then shift data into the daisychained shift registers as an update is needed.

byte dataMap[] = {
0b00111111, // 0 with bits representing DP,g,f,e,d,c,b,a
0b00000110, // 1
0b01011011, // 2
// etc
};


where segments are layed at as

   a
f     b
   g
e     c
   d      DP or colon


then call the array in loop(), make it a function if you want.

digitalWrite (ssPin, LOW); // D10 on Uno, used as Latch signal
for (x = 0; x &lt;4; x=x+1){
SPI.transfer (mapArray[digit0]); // digit0 value mapped to segments
SPI.transfer (mapArray[digit1]);
SPI.transfer (mapArray[digit2]);
SPI.transfer (mapArray[digit3]);
}
digitalWrite (ssPin, LOW); // outputs update on this rising edge


I wonder where DP5, DP6, which make the colon, are? I don't see them in the pinout.