Given below are two statements:

Statement 1: (167) 10=(10100111)2

Statement II: (11010110) 2=(214)10

In the light of the above statements, choose the correct answer from the options given below

The correct option is: Both Statement I and Statement II are true.

Let us verify both statements step-by-step to understand why they are correct.

Step 1: Verify Statement I
Statement I claims that the decimal number 167 is equivalent to the binary number 10100111.
To convert the decimal number (167)₁₀ to binary, we divide by 2 repeatedly and record the remainders from bottom to top:

167 �� 2 = 83 with a remainder of 1
83 ÷ 2 = 41 with a remainder of 1
41 ÷ 2 = 20 with a remainder of 1
20 ÷ 2 = 10 with a remainder of 0
10 ÷ 2 = 5 with a remainder of 0
5 ÷ 2 = 2 with a remainder of 1
2 ÷ 2 = 1 with a remainder of 0
1 ÷ 2 = 0 with a remainder of 1

Reading the remainders from bottom to top gives the binary representation:
10100111
Thus, (167)₁₀ = (10100111)₂. Statement I is true.

Step 2: Verify Statement II
Statement II claims that the binary number 11010110 is equivalent to the decimal number 214.
To convert the binary number (11010110)₂ to decimal, we express it as the sum of powers of 2 multiplied by their corresponding bits:

$$(1\times 2^7)+(1\times 2^6)+(0\times 2^5)+(1\times 2^4)+(0\times 2^3)+(1\times 2^2)+(1\times 2^1)+(0\times 2^0)$$

Calculating the values of the powers of 2:
2⁷ = 128
2⁶ = 64
2⁵ = 32
2⁴ = 16
2³ = 8
2² = 4
2¹ = 2
2⁰ = 1

Substituting these back into the expression:
(1 × 128) + (1 × 64) + (0 × 32) + (1 × 16) + (0 × 8) + (1 × 4) + (1 × 2) + (0 × 1)
= 128 + 64 + 0 + 16 + 0 + 4 + 2 + 0
= 214

Thus, (11010110)₂ = (214)₁₀. Statement II is true.

Since both Statement I and Statement II are correct, the correct option is "Both Statement I and Statement II are true."