Question

Convert each of the following binary representations to its equivalent base ten form.

1. 10101011

Answer 1

Answer: 171

Explanation: 10101011 = 171 Write the binary number and count the power of 2 from right to left, starting from 0 onwards. Now each binary number has the corresponding power of 2 starting from right to left. So the most significant bit will have the highest power of 2. The final answer will be converted into a decimal number that is base 10.

Answer 2

The binary number 10101011 converts to 171 in decimal form by assigning each digit its corresponding power of 2 based on position and summing the resulting values.

Step-by-step explanation:

To convert the binary number 10101011 to its equivalent base ten form, you write out the binary digits and multiply each by the power of 2 that its position represents, starting from the right at position 0.

Then, sum the resulting products.

10101011 in binary equals:

• (1 × 2^7) + (0 × 2^6) + (1 × 2^5) + (0 × 2^4) + (1 × 2^3) + (0 × 2^2) + (1 × 2^1) + (1 × 2^0)
• (128) + (0) + (32) + (0) + (8) + (0) + (2) + (1)
• 171 in base ten

So, the number 10101011 in binary converts to 171 in decimal.