johndg, thank you once again. I extracted one of my L293D from the L293D motor driver shield, and could run my 4 wire stepper forward and backward after placing the L293D on my breadboard, which I believe is a good step for this study. I had lots of cables on the breadboard to have it run. I believe the shield itself has those connections on its circuit. I just need to figure out how the 74HCT595N operates here... So that I can score my goal.
Circuit scheme:
As I have used (4 wire) bipolar stepper motor in my project,
I have connected two joint wires of the bipolar motor to slots of Motor A,
and the other two joint ones to slots of Motor B.

Code for running BP Motor forward:
const int motorPin1 = 5; // Pin 14 of L293D
const int motorPin2 = 6; // Pin 10 of L293D
const int motorPin3 = 10; // Pin 7 of L293D
const int motorPin4 = 9; // Pin 2 of L293D
void setup(){
pinMode(motorPin1, OUTPUT);
pinMode(motorPin2, OUTPUT);
pinMode(motorPin3, OUTPUT);
pinMode(motorPin4, OUTPUT);
}
void loop(){
digitalWrite(motorPin1, HIGH);
digitalWrite(motorPin2, LOW);
digitalWrite(motorPin3, LOW);
digitalWrite(motorPin4, LOW);
delay(5);
digitalWrite(motorPin1, LOW);
digitalWrite(motorPin2, LOW);
digitalWrite(motorPin3, HIGH);
digitalWrite(motorPin4, LOW);
delay(5);
digitalWrite(motorPin1, LOW);
digitalWrite(motorPin2, HIGH);
digitalWrite(motorPin3, LOW);
digitalWrite(motorPin4, LOW);
delay(5);
digitalWrite(motorPin1, LOW);
digitalWrite(motorPin2, LOW);
digitalWrite(motorPin3, LOW);
digitalWrite(motorPin4, HIGH);
delay(5);
}
Code for running BP Motor backward:
const int motorPin1 = 5; // Pin 14 of L293D
const int motorPin2 = 6; // Pin 10 of L293D
const int motorPin3 = 10; // Pin 7 of L293D
const int motorPin4 = 9; // Pin 2 of L293D
void setup(){
pinMode(motorPin1, OUTPUT);
pinMode(motorPin2, OUTPUT);
pinMode(motorPin3, OUTPUT);
pinMode(motorPin4, OUTPUT);
}
void loop(){
digitalWrite(motorPin1, LOW);
digitalWrite(motorPin2, LOW);
digitalWrite(motorPin3, LOW);
digitalWrite(motorPin4, HIGH);
delay(5);
digitalWrite(motorPin1, LOW);
digitalWrite(motorPin2, HIGH);
digitalWrite(motorPin3, LOW);
digitalWrite(motorPin4, LOW);
delay(5);
digitalWrite(motorPin1, LOW);
digitalWrite(motorPin2, LOW);
digitalWrite(motorPin3, HIGH);
digitalWrite(motorPin4, LOW);
delay(5);
digitalWrite(motorPin1, HIGH);
digitalWrite(motorPin2, LOW);
digitalWrite(motorPin3, LOW);
digitalWrite(motorPin4, LOW);
delay(5);
}