Question

What is the equivalent decimal value of the binary number 11001010?

Answer 1

The binary number 11001010 converts to the decimal number 202 by summing each binary digit's value calculated using powers of 2. The binary digits correspond to 128, 64, 8, and 2, which add up to the decimal value 202.

Step-by-step explanation:

The equivalent decimal value of the binary number 11001010 requires converting each binary digit to its decimal value and then summing them up according to their position in the binary number. To convert, we use powers of 2, with the rightmost digit being 2⁰ (which is 1), and then increasing the exponent by 1 as we move leftward.

Here is the step-by-step calculation:

• (1 × 2⁷) + (1 × 2⁶) + (0 × 2⁵) + (0 × 2⁴) + (1 × 2³) + (0 × 2²) + (1 × 2¹) + (0 × 2⁰)
• (1 × 128) + (1 × 64) + (0 × 32) + (0 × 16) + (1 × 8) + (0 × 4) + (1 × 2) + (0 × 1)
• 128 + 64 + 0 + 0 + 8 + 0 + 2 + 0
• 202

Therefore, the equivalent decimal value of the binary number 11001010 is 202.