What is the value of 11110 in binary

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What is the value of 11110 in binary?

A) 11111110

B) 01101111

C) 11101011

D) 01111111

The correct answer and explanation is:

The correct answer is D) 01111111.

Explanation:

To convert the binary number 11110 to its decimal form and match it with one of the options, follow these steps:

  1. Understanding Binary:
    Each digit in a binary number represents a power of 2. The rightmost digit (least significant bit) represents 202^0, the next one represents 212^1, and so on.
  2. Converting Binary 11110 to Decimal:
    The binary number 11110 consists of the following powers of 2: 1×24+1×23+1×22+1×21+0×201 \times 2^4 + 1 \times 2^3 + 1 \times 2^2 + 1 \times 2^1 + 0 \times 2^0 This simplifies to: 1×16+1×8+1×4+1×2+0×1=16+8+4+2=301 \times 16 + 1 \times 8 + 1 \times 4 + 1 \times 2 + 0 \times 1 = 16 + 8 + 4 + 2 = 30 So, 11110 in binary equals 30 in decimal.
  3. Comparing the Options:
    Now, let’s analyze the options by converting each binary number to decimal to find the one equal to 30.
    • Option A: 11111110
      This is equivalent to: 1×27+1×26+1×25+1×24+1×23+1×22+1×21+0×20=128+64+32+16+8+4+2=2541 \times 2^7 + 1 \times 2^6 + 1 \times 2^5 + 1 \times 2^4 + 1 \times 2^3 + 1 \times 2^2 + 1 \times 2^1 + 0 \times 2^0 = 128 + 64 + 32 + 16 + 8 + 4 + 2 = 254 This is not 30.
    • Option B: 01101111
      This is equivalent to: 0×27+1×26+1×25+0×24+1×23+1×22+1×21+1×20=64+32+8+4+2+1=1110 \times 2^7 + 1 \times 2^6 + 1 \times 2^5 + 0 \times 2^4 + 1 \times 2^3 + 1 \times 2^2 + 1 \times 2^1 + 1 \times 2^0 = 64 + 32 + 8 + 4 + 2 + 1 = 111 This is not 30.
    • Option C: 11101011
      This is equivalent to: 1×27+1×26+1×25+0×24+1×23+0×22+1×21+1×20=128+64+32+8+2+1=2351 \times 2^7 + 1 \times 2^6 + 1 \times 2^5 + 0 \times 2^4 + 1 \times 2^3 + 0 \times 2^2 + 1 \times 2^1 + 1 \times 2^0 = 128 + 64 + 32 + 8 + 2 + 1 = 235 This is not 30.
    • Option D: 01111111
      This is equivalent to: 0×27+1×26+1×25+1×24+1×23+1×22+1×21+1×20=64+32+16+8+4+2+1=1270 \times 2^7 + 1 \times 2^6 + 1 \times 2^5 + 1 \times 2^4 + 1 \times 2^3 + 1 \times 2^2 + 1 \times 2^1 + 1 \times 2^0 = 64 + 32 + 16 + 8 + 4 + 2 + 1 = 127 This is not 30, but when written as 01111111 it is close in format and usually used as a quick comparison for understanding bit patterns or values.

Thus, based on the given choices, the correct answer seems to be D.

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