If $(11011)_2 = (\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_)_{10}$ , then the number in the blank space is

Q: If $(11011)_2 = (\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_)_{10}$ , then the number in the blank space is

To determine the decimal equivalent of the binary number $ (11011)_2 $, we need to convert it from base 2 to base 10. Here's how we can do that: The binary number $ 11011_2 $ can be expanded as follows: \[ 11011_2 = 1 \times 2^4 + 1 \times 2^3 + 0 \times 2^2 + 1 \times 2^1 + 1 \times 2^0 \] Calculating each term: - $ 1 \times 2^4 = 16 $ - $ 1 \times 2^3 = 8 $ - $ 0 \times 2^2 = 0 $ - $ 1 \times 2^1 = 2 $ - $ 1 \times 2^0 = 1 $ Adding these values together gives: \[ 16 + 8 + 0 + 2 + 1 = 27 \] Therefore, the decimal equivalent of the binary number $ 11011_2 $ is $ 27 $. Now, let's explain why Option 2 is correct and why the other options are incorrect: 1. **Option 1: 22** - This is incorrect because the calculation of the binary to decimal conversion does not sum to 22. As shown above, the correct sum is 27. 2. **Option 2: 27** - This is the correct answer. The detailed conversion process clearly shows that the binary number $ 11011_2 $ equals 27 in decimal. 3. **Option 3: 30** - This is incorrect because the sum of the powers of 2, as calculated, does not equal 30. The correct sum is 27. 4. **Option 4: 33** - This is incorrect because the conversion process does not yield 33. The correct result of the conversion is 27. In conclusion, the correct decimal equivalent of the binary number $ 11011_2 $ is indeed 27, which corresponds to Option 2.

Question

Accepted Answer

To determine the decimal equivalent of the binary number $ (11011)_2 $, we need to convert it from base 2 to base 10. Here's how we can do that:

The binary number $ 11011_2 $ can be expanded as follows:

$$
11011_2 = 1 \times 2^4 + 1 \times 2^3 + 0 \times 2^2 + 1 \times 2^1 + 1 \times 2^0
$$

Calculating each term:

- $ 1 \times 2^4 = 16 $
- $ 1 \times 2^3 = 8 $
- $ 0 \times 2^2 = 0 $
- $ 1 \times 2^1 = 2 $
- $ 1 \times 2^0 = 1 $

Adding these values together gives:

$$
16 + 8 + 0 + 2 + 1 = 27
$$

Therefore, the decimal equivalent of the binary number $ 11011_2 $ is $ 27 $.

Now, let's explain why Option 2 is correct and why the other options are incorrect:

1. **Option 1: 22** - This is incorrect because the calculation of the binary to decimal conversion does not sum to 22. As shown above, the correct sum is 27.

2. **Option 2: 27** - This is the correct answer. The detailed conversion process clearly shows that the binary number $ 11011_2 $ equals 27 in decimal.

3. **Option 3: 30** - This is incorrect because the sum of the powers of 2, as calculated, does not equal 30. The correct sum is 27.

4. **Option 4: 33** - This is incorrect because the conversion process does not yield 33. The correct result of the conversion is 27.

In conclusion, the correct decimal equivalent of the binary number $ 11011_2 $ is indeed 27, which corresponds to Option 2.