A. The Binary Number System:
The binary number system is a numeral system that uses only two digits, 0 and 1. It is the fundamental numbering system used in computers and digital systems. Each digit in a binary number represents a power of 2, with the rightmost digit being 2^0, the next being 2^1, then 2^2, and so on.
B. The Decimal Number System:
The decimal number system, also known as the base-10 system, is the most common numeral system used by humans. It uses 10 different digits, 0 to 9, and each digit represents a power of 10, with the rightmost digit being 10^0, the next being 10^1, then 10^2, and so on.
C. Binary to Decimal Conversion:
Binary to decimal conversion is the process of converting a binary number (base-2) to its equivalent decimal representation (base-10).
D. Steps to Convert Binary to Decimal Numbers:
1. Start from the rightmost digit (also known as the least significant bit) of the binary number.
2. Assign each digit a power of 2, starting with 2^0 for the rightmost digit, 2^1 for the next digit, 2^2 for the next, and so on.
3. Multiply each binary digit with its respective power of 2.
4. Sum up all the results obtained in step 3 to get the decimal equivalent.
Alternatively, a quicker approach is using the following formula:
1. Let n be the number of digits in the binary number.
2. For the i-th digit from the right (starting with i = 0), multiply the digit by 2 raised to the power of i.
3. Sum up all the results obtained in step 2.
For example, to convert the binary number 1011 to decimal:
Using the formula:
1. n = 4 (number of digits)
2. (1 * 2^3) + (0 * 2^2) + (1 * 2^1) + (1 * 2^0) = 8 + 0 + 2 + 1 = 11.
Using the step-by-step approach:
1. Start from the rightmost digit: 1.
2. Assign powers of 2: 2^3, 2^2, 2^1, 2^0.
3. Multiply each digit by its respective power of 2: (1 * 2^3) = 8.
4. Move to the next digit: 0.
5. Multiply by its respective power of 2: (0 * 2^2) = 0.
6. Move to the next digit: 1.
7. Multiply by its respective power of 2: (1 * 2^1) = 2.
8. Move to the next digit: 1.
9. Multiply by its respective power of 2: (1 * 2^0) = 1.
10. Sum up all the results: 8 + 0 + 2 + 1 = 11.
Therefore, the binary number 1011 is equal to the decimal number 11.
Explains the conversion of a binary number (base-2) to an equivalent
decimal number (base-10).
a. What is a Binary Number System?
b. 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.
1 answer