What is the value of the binary number 101 in the decimal number system?a)3b)4c)5d)6e)7Correct answer is option 'C'. Can you explain this answer?

Question

Answer

Conversion from Binary to Decimal

To convert a binary number to a decimal number, each digit in the binary number is multiplied by the corresponding power of 2 and then added together.

For example, let's convert the binary number 101 to decimal.

Step 1: Assign Powers of 2

We start by assigning powers of 2 to each digit in the binary number, from right to left. For a binary number with n digits, the rightmost digit is assigned a power of 2 equal to 2^0, the next digit is assigned a power of 2 equal to 2^1, and so on.

In this case, we have three digits in the binary number 101, so we assign powers of 2 as follows:
- The rightmost digit (1) is assigned a power of 2 equal to 2^0 = 1.
- The middle digit (0) is assigned a power of 2 equal to 2^1 = 2.
- The leftmost digit (1) is assigned a power of 2 equal to 2^2 = 4.

Step 2: Multiply and Sum

Next, we multiply each digit of the binary number by its corresponding power of 2 and sum the results.

For the binary number 101, the calculation is as follows:
1 * 4 + 0 * 2 + 1 * 1 = 4 + 0 + 1 = 5.

Therefore, the decimal value of the binary number 101 is 5.

Conclusion

The correct answer is option C) 5.

Answer

The value of (101)2

101²is calculated in decimal number system as below:

(101)²= (1 × 2)²+ (0 × 2)¹+ (1 × 2)⁰

= 4 + 0 + 1

= 5

The value is 5

So, 5 is the value of the binary number 101 in the decimal number system.

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