Decimal System (Base-10)

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The decimal system, also known as the base-10 numeral system, is the most common numeral system used by humans. It’s called “decimal” because it is based on powers of 10. In the decimal system, there are ten unique symbols, commonly represented by the digits 0 to 9.

Each position in a decimal number represents a power of 10. The rightmost digit represents the “ones” place, the next digit to the left represents the “tens” place, the next represents the “hundreds” place, and so on.

For example, the number “253” in the decimal system can be understood as:

• The digit 3 represents 3 ones (3 x 10^0).
• The digit 5 represents 5 tens (5 x 10^1).
• The digit 2 represents 2 hundreds (2 x 10^2).

When these values are added together, they yield the total value of 253.

The decimal system is widely used for everyday counting and calculations, as it is intuitive for humans. It’s used in various fields such as mathematics, finance, and everyday activities like measuring, currency, and time.

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Let’s create a simple coding example in Python to convert a decimal number to its binary representation and then display the conversion in a table format.

def decimal_to_binary(decimal_num):
    binary_num = bin(decimal_num)[2:]  # Convert decimal to binary and remove the "0b" prefix
    return binary_num

# Example decimal numbers
decimal_numbers = [10, 25, 42, 87, 128]

# Display the conversion in a table format
print("{:^10} | {:^15}".format("Decimal", "Binary"))
print("-" * 28)
for decimal_num in decimal_numbers:
    binary_num = decimal_to_binary(decimal_num)
    print("{:^10} | {:^15}".format(decimal_num, binary_num))

Output:

 Decimal  |     Binary     
----------------------------
    10     |       1010     
    25     |      11001     
    42     |      101010    
    87     |      1010111   
   128     |     10000000   

In this example, the decimal_to_binary function converts a decimal number to its binary representation using the built-in bin function and then removes the “0b” prefix. The code then demonstrates how to create a table to display the decimal numbers and their binary equivalents using formatted output.

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