What is the decimal equal to the square root of a number whose binary representation is 1100100?

Given:

A number whose binary representation is 1100100

Formula used:

To convert binary into decimal-

(Decimal number)₁₀ = (d₀ × 2⁰) + (d₁ × 2¹) + ...... + (d_n-1 × 2^n-1)

where d_{0 ,} d₁ are individual digits of the binary number starting from the right most position.

Calculation:

Step 1

Write down the binary number 1100100

Step 2

Multiply each digit of the binary number by the corresponding power if 2

⇒ 1 × 2⁶ + 1 × 2⁵ + 0 × 2⁴ + 0 × 2³ + 1 × 2² + 0 × 2¹ + 0 × 2⁰

Step 3

Solve the power

⇒ 64 + 32 + 0 + 0 + 4 + 0 + 0 = 100

So, the decimal number is 100

The square root of 100 = 10

∴ Option C is correct.