Oh gosh, what have I gotten myself into! I was looking through the code and it the language definately looks fairly straight forward.
This is the code I quickly uploaded to test the idea. I'm going to set it up again and try it again but last time it counted so weirdly and far to fast. I think it's meant for only hour and minute display though, as well as it being 24 hours but the 24 vs 12 hours can be relatively easily changed.
/*
An open-source binary clock for Arduino.
Based on the code from by Rob Faludi (http://www.faludi.com)
Code under (cc) by Daniel Spillere Andrade, www.danielandrade.net
http://creativecommons.org/license/cc-gpl
*/
int second=0, minute=0, hour=0; //start the time on 00:00:00
int munit,hunit,valm=0,valh=0,ledstats,i;
void setup() { //set outputs and inputs
pinMode(1, OUTPUT);pinMode(2, OUTPUT);pinMode(3, OUTPUT);pinMode(4, OUTPUT);pinMode(5, OUTPUT);
pinMode(6, OUTPUT);pinMode(7, OUTPUT);pinMode(8, OUTPUT);pinMode(9, OUTPUT);pinMode(10, OUTPUT);
pinMode(11, OUTPUT);pinMode(12, OUTPUT);pinMode(13, OUTPUT);
pinMode(0, INPUT);
}
void loop() {
static unsigned long lastTick = 0; // set up a local variable to hold the last time we moved forward one second
// (static variables are initialized once and keep their values between function calls)
// move forward one second every 1000 milliseconds
if (millis() - lastTick >= 1000) {
lastTick = millis();
second++;
}
// move forward one minute every 60 seconds
if (second >= 60) {
minute++;
second = 0; // reset seconds to zero
}
// move forward one hour every 60 minutes
if (minute >=60) {
hour++;
minute = 0; // reset minutes to zero
}
if (hour >=24) {
hour=0;
minute = 0; // reset minutes to zero
}
munit = minute%10; //sets the variable munit and hunit for the unit digits
hunit = hour%10;
ledstats = digitalRead(0); // read input value, for setting leds off, but keeping count
if (ledstats == LOW) {
for(i=1;i< =13;i++){
digitalWrite(i, LOW);}
} else {
//minutes units
if(munit == 1 || munit == 3 || munit == 5 || munit == 7 || munit == 9) { digitalWrite(1, HIGH);} else { digitalWrite(1,LOW);}
if(munit == 2 || munit == 3 || munit == 6 || munit == 7) {digitalWrite(2, HIGH);} else {digitalWrite(2,LOW);}
if(munit == 4 || munit == 5 || munit == 6 || munit == 7) {digitalWrite(3, HIGH);} else {digitalWrite(3,LOW);}
if(munit == 8 || munit == 9) {digitalWrite(4, HIGH);} else {digitalWrite(4,LOW);}
//minutes
if((minute >= 10 && minute < 20) || (minute >= 30 && minute < 40) || (minute >= 50 && minute < 60)) {digitalWrite(5, HIGH);} else {digitalWrite(5,LOW);}
if(minute >= 20 && minute < 40) {digitalWrite(6, HIGH);} else {digitalWrite(6,LOW);}
if(minute >= 40 && minute < 60) {digitalWrite(7, HIGH);} else {digitalWrite(7,LOW);}
//hour units
if(hunit == 1 || hunit == 3 || hunit == 5 || hunit == 7 || hunit == 9) {digitalWrite(8, HIGH);} else {digitalWrite(8,LOW);}
if(hunit == 2 || hunit == 3 || hunit == 6 || hunit == 7) {digitalWrite(9, HIGH);} else {digitalWrite(9,LOW);}
if(hunit == 4 || hunit == 5 || hunit == 6 || hunit == 7) {digitalWrite(10, HIGH);} else {digitalWrite(10,LOW);}
if(hunit == 8 || hunit == 9) {digitalWrite(11, HIGH);} else {digitalWrite(11,LOW);}
//hour
if(hour >= 10 && hour < 20) {digitalWrite(12, HIGH);} else {digitalWrite(12,LOW);}
if(hour >= 20 && hour < 24) {digitalWrite(13, HIGH);} else {digitalWrite(13,LOW);}
}
valm = analogRead(0); // add one minute when pressed
if(valm<800) {
minute++;
second=0;
delay(250);
}
valh = analogRead(5); // add one hour when pressed
if(valh<800) {
hour++;
second=0;
delay(250);
}
}
So when I get home I'm going to try putting parts of your code into this. But at that point, I need help on how to assign the A0-A5 pins so I can have seconds as well. And also, why is Pin0 an input? What is being inputted? If I can use my 1hz crystal oscillator there that would be great. I have a pretty accurate frequency on it so long as the clock as at room temperature.
I'm not familiar with an 8 bit shift registrar. I see how it can act as both the 10digit and 1digit though. If this chip is meant to be used outside the arduino I would end up needing a few 4 input NAND gates. Unless the arduino can act as that.. I'm sure it can. Oh boy, this is a lot of information to cram in. I gotta crank it out by the end of the week. Afterwards I can take more time to enjoy the possibilities of the arduino though as I finish building my LED cube 
Ok so I tested my highvoltage supply and the tubes light up great. So if I can get the arduino working (5 volt outputs right?) then I'll have this clock up and running in no time. Gonna be a lot of soldering in my future.