BINARY TO DECIMAL CONVERSION:
a.What is a Binary Number System?
c.What is Binary to Decimal Conversion?
d.How to Convert Binary to Decimal Numbers?Describe the stepsof
I.Explains the conversion of a binary number (base-2) to an equivalent
decimal number (base-10).
b.What is a Decimal Number System?
differentformulas to perform the conversion.
a. The Binary Number System is a number system that uses only two digits, 0 and 1. It is also known as the base-2 number system as it represents numbers using only two digits.
c. Binary to Decimal Conversion is the process of converting a binary number to its equivalent decimal representation. In the decimal system, we use 10 digits (0-9), while in the binary system, we use only 2 digits (0 and 1).
d. To convert a binary number to a decimal number, follow these steps:
1. Start from the rightmost digit of the binary number.
2. Assign a power of 2 to each digit, starting from 2^0 for the rightmost digit, and increasing the power by 1 for each subsequent digit.
3. Multiply each digit with its corresponding power of 2.
4. Sum up all the products obtained in step 3 to get the decimal equivalent of the binary number.
For example, let's convert the binary number 101010 to its decimal equivalent:
Starting from the rightmost digit:
2^0 * 0 = 0
2^1 * 1 = 2
2^2 * 0 = 0
2^3 * 1 = 8
2^4 * 0 = 0
2^5 * 1 = 32
Summing up the products:
0 + 2 + 0 + 8 + 0 + 32 = 42
Therefore, the decimal equivalent of the binary number 101010 is 42.
b. The Decimal Number System, also known as the base-10 number system, is the most commonly used number system in everyday life. It uses 10 digits (0-9) to represent numbers. The value of each digit is determined by its position in the number, where the rightmost digit represents the units place, the next digit represents the tens place, the following digit represents the hundreds place, and so on.
Different formulas to perform the conversion:
1. Formula 1:
To convert a binary number to a decimal number, use the formula:
decimal = (dn * 2^n) + (dn-1 * 2^(n-1)) + ... + (d2 * 2^2) + (d1 * 2^1) + (d0 * 2^0),
where dn, dn-1, ..., d1, d0 are the binary digits from right to left, and n is the total number of digits.
2. Formula 2:
Another formula to convert binary to decimal is to multiply each digit by the corresponding power of 2 and then sum up the products.
decimal = (d0 * 2^0) + (d1 * 2^1) + ... + (dn * 2^n).