computer_science_concepts.md

From Bits to Bytes to Data Types

• A bit can have 2 states ("off" and "on") and therefore can store 2 values (0 and 1).
  • Therefore, 2 bits can have 4 distinct combinations of states and therefore 4 distince values (00, 01, 10, 11).
    • This pattern continues. There are $2^N$ unique states when working with $N$ bits:
      • 1 bits = $2^1$ = 2 distinct combinations, therefore 2 states.
      • 2 bits = $2^2$ = 4 distinct combinations, therefore 4 states.
      • 3 bits = $2^3$ = 8 distinct combinations, therefore 8 states.
      • 4 bits = $2^4$ = 16 distinct combinations, therefore 16 states.
      • 5 bits = $2^5$ = 32 distinct combinations, therefore 32 states.
      • 6 bits = $2^6$ = 64 distinct combinations, therefore 64 states.
      • 7 bits = $2^7$ = 128 distinct combinations, therefore 128 states.
      • 8 bits = $2^8$ = 256 distinct combinations, therefore 256 states.
• 8 bits is equal to 1 byte.
  • Therefore 1 byte can store 256 unique values.

From Data Types to Bytes to Bits

4294967295 / 2

INT | 4,294,967,295 (unsigned) INT | 2,147,483,647 (signed)

BIGINT | 18,446,744,073,709,551,615 (unsigned) BIGINT | 9,223,372,036,854,775,807 (signed)

Recursion

Linear Recursive Process

• A linear recursive process is one that has one base condition/references itself once.
• Example:

def factorial(n):
    if n == 0:
        return 1
    else:
        return n * factorial(n-1)

Tree-Recursive Process

• A tree-recursive process is one that has more than one base condition/references itself more than once
• Example:

def Fib(n):
    if n == 0:
        return 0
    elif n == 1:
        return 1
    else:
        return Fib(n-1) + Fib(n-2)

This process can be represented with the following structure:

Question to self (2021-08-31):

• Is the number of base conditions/axioms always equal to the number of times the procedure references itself in the function/procedure definition?

Ramblings...

Take the following program:

user_input = int( input('What is your favorite number? ') )
print(f"{user_input**2} is the square of your favorite number.")

this program is run by running:

$ python tmp.py 
What is your favorite number? 23
529 is the square of your favorite number.

• The number 23 is the user input to the programmer-defined tmp.py program...
  • The program tmp.py is the input to the higher-order programmer defined program python...
    • The higher-order programmer defined program python tmp.py is the input to...what