Зміст курсу

Numeral Systems 101

1. Binary Numeral System

Welcome on Board!Get Acquainted with Binary Code Decipher Binary Number Decipher List of Binary Numbers Cipher Some Numbers Hone your Ciphering Skills Dates in Binary

2. Octal Numeral system

Get Acquainted with the Octal Numeral System Practice Ciphering

3. Hexadecimal Numeral system

Deciphering Challenge One More Ciphering Challenge

4. Revelation

Write the Code in One Line Harder Converting Converting Using Format Method

Get Acquainted with the Octal Numeral System

There is another numeral system called octal. In comparison to binary or decimal, it consists of 8 digits, starting with zero: 0,1,2,3,4,5,6,7.

If you wonder why it was implemented, I want to clarify something.

Usage

As you remember the number in binary representation consists of several digits, one bite for each of them; but in an octal numeral system, three binary digits represent one octal. Therefore, you can represent one word for the computer using fewer symbols. Enormous strings of binary code can be represented in a more beautiful way for the computer; hence, less memory is filled. The principle of converting a number to the decimal system from octal one is the same as with binary:As you remember the number in binary representation consists of several digits, one bite for each of them; but in an octal numeral system, three binary digits represent one octal. Therefore, you can represent one word for the computer using fewer symbols. Enormous strings of binary code can be represented in a more beautiful way for the computer; hence, less memory is filled. The principle of converting a number to the decimal system from octal one is the same as with binary:

Rule

Algorithms of converting to decimal numeral system overlap for different numeral systems. Here is the same for octal number 221: the index of the left number 2 is 2, the index of the middle number 2 is 1 and the index of the number 1 is zero; but here we should multiply the numbers by 8 raised to the power of index. Hence, 221-> 2*8^2+2*8^1+2*8^0=128+16+2=146.


              12345678910111213141516171819202122
            
#  Defining the octal number
octal_number = 221
# Creating a variable for storing the converted decimal number
decimal_number = 0
# The text should be realised here due to the reason that further the binary number will be changed
print("The number in octal numeral system is: ", octal_number)
# Creating value for working with the power of a number
power = 0
# The loop executes till the number is not null
while octal_number != 0:
    # Separating the last digit of octal_number using the remainder of the division operation
    last_digit = octal_number % 10
    # Multiply last_digit by 8 raised to the relevant power
    result = last_digit * pow(8, power)
    # Adding the result to the decimal number 
    decimal_number = decimal_number + result
    # This operation of integer division decreases a number and put aside the last digit that was already used
    octal_number = octal_number // 10
    # Increasing iterator to work with the power
    power = power + 1
# Printing the result
print("The number in decimal numeral system is: ", decimal_number)

Завдання

Doing as many tasks as possible is a recipe for success! Write the code that will decode the number 117 from the octal numeral system to decimal. Fill the gaps and follow the algorithm. If everything is correct you will receive one special number 🧐 But the explanation is waiting for you at the end of this chapter.

Print the octal_number.
Define the loop which goes through the octal_number variable till it is zero.
Assign the remainder of division octal_number by 10 to the variable last_digit.
Multiply the received last_digit by the 8 raised to the relevant power.
Decrease the octal_number using integer division by 10.
Increase the power by 1.
Print the decimal_number.

Завдання

Print the octal_number.
Define the loop which goes through the octal_number variable till it is zero.
Assign the remainder of division octal_number by 10 to the variable last_digit.
Multiply the received last_digit by the 8 raised to the relevant power.
Decrease the octal_number using integer division by 10.
Increase the power by 1.
Print the decimal_number.

Note
I think you received 142857 which is called a cyclic number. Let me explain why:142857 x 1 = 142857 142857 x 2 = 285714 142857 x 3 = 428571 142857 x 4 = 571428 142857 x 5 = 714285 142857 x 6 = 857142. As you can recognize such multiplication results in a new number that is the same, but digits located in a different order; it creates a cycle. Another interesting fact for you🙄.

Перейдіть на комп'ютер для реальної практикиПродовжуйте з того місця, де ви зупинились, використовуючи один з наведених нижче варіантів

Все було зрозуміло?

Секція 2. Розділ 1

Get Acquainted with the Octal Numeral System

There is another numeral system called octal. In comparison to binary or decimal, it consists of 8 digits, starting with zero: 0,1,2,3,4,5,6,7.

If you wonder why it was implemented, I want to clarify something.

Usage

Rule


              12345678910111213141516171819202122
            
#  Defining the octal number
octal_number = 221
# Creating a variable for storing the converted decimal number
decimal_number = 0
# The text should be realised here due to the reason that further the binary number will be changed
print("The number in octal numeral system is: ", octal_number)
# Creating value for working with the power of a number
power = 0
# The loop executes till the number is not null
while octal_number != 0:
    # Separating the last digit of octal_number using the remainder of the division operation
    last_digit = octal_number % 10
    # Multiply last_digit by 8 raised to the relevant power
    result = last_digit * pow(8, power)
    # Adding the result to the decimal number 
    decimal_number = decimal_number + result
    # This operation of integer division decreases a number and put aside the last digit that was already used
    octal_number = octal_number // 10
    # Increasing iterator to work with the power
    power = power + 1
# Printing the result
print("The number in decimal numeral system is: ", decimal_number)

Завдання

Print the octal_number.
Define the loop which goes through the octal_number variable till it is zero.
Assign the remainder of division octal_number by 10 to the variable last_digit.
Multiply the received last_digit by the 8 raised to the relevant power.
Decrease the octal_number using integer division by 10.
Increase the power by 1.
Print the decimal_number.

Завдання

Print the octal_number.
Define the loop which goes through the octal_number variable till it is zero.
Assign the remainder of division octal_number by 10 to the variable last_digit.
Multiply the received last_digit by the 8 raised to the relevant power.
Decrease the octal_number using integer division by 10.
Increase the power by 1.
Print the decimal_number.

Note
I think you received 142857 which is called a cyclic number. Let me explain why:142857 x 1 = 142857 142857 x 2 = 285714 142857 x 3 = 428571 142857 x 4 = 571428 142857 x 5 = 714285 142857 x 6 = 857142. As you can recognize such multiplication results in a new number that is the same, but digits located in a different order; it creates a cycle. Another interesting fact for you🙄.

Все було зрозуміло?

Секція 2. Розділ 1

Get Acquainted with the Octal Numeral System

There is another numeral system called octal. In comparison to binary or decimal, it consists of 8 digits, starting with zero: 0,1,2,3,4,5,6,7.

If you wonder why it was implemented, I want to clarify something.

Usage

Rule


              12345678910111213141516171819202122
            
#  Defining the octal number
octal_number = 221
# Creating a variable for storing the converted decimal number
decimal_number = 0
# The text should be realised here due to the reason that further the binary number will be changed
print("The number in octal numeral system is: ", octal_number)
# Creating value for working with the power of a number
power = 0
# The loop executes till the number is not null
while octal_number != 0:
    # Separating the last digit of octal_number using the remainder of the division operation
    last_digit = octal_number % 10
    # Multiply last_digit by 8 raised to the relevant power
    result = last_digit * pow(8, power)
    # Adding the result to the decimal number 
    decimal_number = decimal_number + result
    # This operation of integer division decreases a number and put aside the last digit that was already used
    octal_number = octal_number // 10
    # Increasing iterator to work with the power
    power = power + 1
# Printing the result
print("The number in decimal numeral system is: ", decimal_number)

Завдання

Print the octal_number.
Define the loop which goes through the octal_number variable till it is zero.
Assign the remainder of division octal_number by 10 to the variable last_digit.
Multiply the received last_digit by the 8 raised to the relevant power.
Decrease the octal_number using integer division by 10.
Increase the power by 1.
Print the decimal_number.

Завдання

Print the octal_number.
Define the loop which goes through the octal_number variable till it is zero.
Assign the remainder of division octal_number by 10 to the variable last_digit.
Multiply the received last_digit by the 8 raised to the relevant power.
Decrease the octal_number using integer division by 10.
Increase the power by 1.
Print the decimal_number.

Note
I think you received 142857 which is called a cyclic number. Let me explain why:142857 x 1 = 142857 142857 x 2 = 285714 142857 x 3 = 428571 142857 x 4 = 571428 142857 x 5 = 714285 142857 x 6 = 857142. As you can recognize such multiplication results in a new number that is the same, but digits located in a different order; it creates a cycle. Another interesting fact for you🙄.

Все було зрозуміло?

There is another numeral system called octal. In comparison to binary or decimal, it consists of 8 digits, starting with zero: 0,1,2,3,4,5,6,7.

If you wonder why it was implemented, I want to clarify something.

Usage

Rule


              12345678910111213141516171819202122
            
#  Defining the octal number
octal_number = 221
# Creating a variable for storing the converted decimal number
decimal_number = 0
# The text should be realised here due to the reason that further the binary number will be changed
print("The number in octal numeral system is: ", octal_number)
# Creating value for working with the power of a number
power = 0
# The loop executes till the number is not null
while octal_number != 0:
    # Separating the last digit of octal_number using the remainder of the division operation
    last_digit = octal_number % 10
    # Multiply last_digit by 8 raised to the relevant power
    result = last_digit * pow(8, power)
    # Adding the result to the decimal number 
    decimal_number = decimal_number + result
    # This operation of integer division decreases a number and put aside the last digit that was already used
    octal_number = octal_number // 10
    # Increasing iterator to work with the power
    power = power + 1
# Printing the result
print("The number in decimal numeral system is: ", decimal_number)

Завдання

Print the octal_number.
Define the loop which goes through the octal_number variable till it is zero.
Assign the remainder of division octal_number by 10 to the variable last_digit.
Multiply the received last_digit by the 8 raised to the relevant power.
Decrease the octal_number using integer division by 10.
Increase the power by 1.
Print the decimal_number.

Note
I think you received 142857 which is called a cyclic number. Let me explain why:142857 x 1 = 142857 142857 x 2 = 285714 142857 x 3 = 428571 142857 x 4 = 571428 142857 x 5 = 714285 142857 x 6 = 857142. As you can recognize such multiplication results in a new number that is the same, but digits located in a different order; it creates a cycle. Another interesting fact for you🙄.

Секція 2. Розділ 1