What is a Decimal Number System?
c. What is Binary to Decimal Conversion?
d. How to Convert Binary to Decimal Numbers? Describe the steps of
different formulas to perform the conversion.�
a. The Decimal Number System is a base-10 number system that uses ten digits (0-9) to represent all possible numbers. Each digit in a decimal number has a positional value based on its position from the right, with the rightmost digit being the units place, the next digit to the left being the tens place, and so on.
b. Binary to Decimal Conversion is the process of converting a binary number (base-2) to its equivalent decimal representation (base-10).
c. To convert a binary number to its decimal equivalent, follow these steps:
Step 1: Write down the binary number.
Step 2: Assign a positional value to each digit starting from the right. The rightmost digit has a positional value of 2^0 (1), the next digit to the left has a positional value of 2^1 (2), the next digit has a positional value of 2^2 (4), and so on. The positional values increase by powers of 2 from right to left.
Step 3: Multiply each digit of the binary number by its positional value.
Step 4: Sum up the products from Step 3 to get the decimal equivalent.
For example, let's convert the binary number 1010 to decimal:
Step 1: Write down the binary number: 1010.
Step 2: Assign positional values to each digit: 2^3 (8), 2^2 (4), 2^1 (2), 2^0 (1).
Step 3: Multiply each digit by its positional value: 1 * 8, 0 * 4, 1 * 2, 0 * 1.
Step 4: Sum up the products: 8 + 0 + 2 + 0 = 10.
Therefore, the binary number 1010 is equivalent to the decimal number 10.
There are also shortcut formulas that can be used for converting binary to decimal. One such formula is:
Decimal = (d1 * 2^(n-1)) + (d2 * 2^(n-2)) + ... + (dn * 2^0)
Where d1 to dn represents the digits of the binary number from left to right and n represents the total number of digits in the binary number. Using this formula, you can directly calculate the decimal equivalent without going through the step-by-step multiplication process.