Testing the bit bang serial transmission to connect the Trinket with the Serial LCD Module 16×2 from NKC Electronics.
The first Sketch with string functions use 3,634 bytes, the second Sketch, avoiding string functions, use 1,362 bytes.

20140217_125246

Sketch with string functions:

/*	Test_LCD.ino
	Arduining.com  16 FEB 2014
	Binary sketch size: 3,634 bytes (of a 5,310 byte maximum)

	A timer is implemented presenting minutes and seconds elapsed since start.
	Bit Banging Serial transmission at 9600 bauds.
	Example using the Trinket from Adafruit (5V, 8 Mhz)
	and Serial LCD Module 16x2 from NKC Electronics.
*/

//----- defining bit banging serial values:------------------------------------
#define	TXDATA    1         // Pin used to transmit data.
#define BITTIME   93        // Adjusted with osciloscope to obtain 9600 bauds.

//----------variables:---------------------------------------------------------
int 	seconds= 0;		//seconds counter
String 	number;			//String to be sent to the display.
//=============================================================================
void setup() {                
	pinMode(TXDATA, OUTPUT);   // initialize the TXDATA pin as an output.
	digitalWrite(TXDATA,HIGH); // TXDATA = 5V when is resting.
//---LCD Display initialisation---
	delay(500);
	sendChar(0xFE);
	sendChar(0x41);		//display on.
	sendChar(0xFE);
	sendChar(0x51);		//clear display.
	sendChar(0xFE);
	sendChar(0x4C);		//cursor blinking Off.
	sendChar(0xFE);
	sendChar(0x48);		//cursor Off.
	sendChar(0xFE);
	sendChar(0x46);		//cursor at home.
	sendChar(0xFE);
	sendChar(0x53);		//backlight brightness command.
	sendChar(4);		//brightness 1-8
	sendChar(0xFE);
	sendChar(0x52);		//contrast command.
	sendChar(45);		//contrast 1-50
	show(" Arduining.com");
}

//================= Main loop =================================================
void loop() {
	if ((millis() % 1000)<2){ 				//Skip until the next second.

		sendChar(0xFE);
		sendChar(0x45);						// Set cursor at
		sendChar(0x45);						// line 2 pos 6

		number = String (seconds/60);		//elapsed minutes
		while(number.length()<2)number= "0" + number;   //format to 2 characters.
		show(number); 						//Show minutes in the display

		sendChar(':');

		number = String (seconds % 60);		//elapsed seconds
		while(number.length()<2)number= "0" + number;   //format to 2 characters.
		show(number); 						//Show seconds in the display

   		seconds++;
   		if (seconds >= 3600) seconds=0;		//roll over
	}
}

//-----------------------------------------------------------------------------
void sendChar(char c){
	delayMicroseconds(BITTIME*2);          		// wait 2 Stop bits.
	digitalWrite(TXDATA,LOW);              		// TXDATA=0.
	delayMicroseconds(BITTIME);            		// wait Start bit.
	for (int i=0; i<8;i++){
		digitalWrite(TXDATA,bitRead(c, i)); 	// bit out.
		delayMicroseconds(BITTIME);          	// wait bit
	}
	digitalWrite(TXDATA,HIGH);            		//TXDATA=1.
}

//-----------------------------------------------------------------------------
void show(String s){
	int lenght=s.length();
	for(int i=0;i<lenght;i++){
	sendChar(s[i]);
	}
}

Sketch without string functions:

/*	Test_LCD_01.ino
	Arduining.com  17 FEB 2014
	Based in Test_LCD.ino (2,278 bytes less avoiding string functions).
	Binary sketch size: 1,356 bytes (of a 5,310 byte maximum)

	A timer is implemented presenting minutes and seconds elapsed since start.
	Bit Banging Serial transmission at 9600 bauds.
	Example using the Trinket from Adafruit (5V, 8 Mhz)
	and Serial LCD Module 16x2 from NKC Electronics.
*/

//----- defining bit banging serial values:------------------------------------
#define	TXDATA    1         // Pin used to transmit data.
#define BITTIME   93        // Adjusted with osciloscope to obtain 9600 bauds.

//----------variables:---------------------------------------------------------
int 	seconds= 0;		//seconds counter
//=============================================================================
void setup() {                
	pinMode(TXDATA, OUTPUT);   // initialize the TXDATA pin as an output.
	digitalWrite(TXDATA,HIGH); // TXDATA = 5V when is resting.
//---LCD Display initialisation---
	delay(500);
	sendChar(0xFE);
	sendChar(0x41);		//display on.
	sendChar(0xFE);
	sendChar(0x51);		//clear display.
	sendChar(0xFE);
	sendChar(0x4C);		//cursor blinking Off.
	sendChar(0xFE);
	sendChar(0x48);		//cursor Off.
	sendChar(0xFE);
	sendChar(0x46);		//cursor at home.
	sendChar(0xFE);
	sendChar(0x53);		//backlight brightness command.
	sendChar(4);		//brightness 1-8
	sendChar(0xFE);
	sendChar(0x52);		//contrast command.
	sendChar(45);		//contrast 1-50
	show(" Arduining.com");
}

//================= Main loop =================================================
void loop() {
	if ((millis() % 1000)<2){ 				//Skip until the next second.

		sendChar(0xFE);
		sendChar(0x45);						// Set cursor at
		sendChar(0x45);						// line 2 pos 6

		sendChar((seconds/600)+'0');		//show tens of minutes 
		sendChar(((seconds/60) % 10)+'0');	//show units of minutes
		sendChar(':');
		sendChar(((seconds % 60)/10)+'0');	//show tens of seconds
		sendChar((seconds % 10)+'0');		//show units of seconds
   		seconds++;
   		if (seconds >= 3600) seconds=0;		//roll over
	}
}

//-----------------------------------------------------------------------------
void sendChar(char c){
	delayMicroseconds(BITTIME*2);          		// wait 2 Stop bits.
	digitalWrite(TXDATA,LOW);              		// TXDATA=0.
	delayMicroseconds(BITTIME);            		// wait Start bit.
	for (int i=0; i<8;i++){
		digitalWrite(TXDATA,bitRead(c, i)); 	// bit out.
		delayMicroseconds(BITTIME);          	// wait bit
	}
	digitalWrite(TXDATA,HIGH);            		//TXDATA=1.
}

//-----------------------------------------------------------------------------
void show(char s[]){
	int i=0;
	while(s[i]!=0){					//looking for the string end.
		sendChar(s[i]);
		i++	;
	}
}
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