The binary equivalent of the decimal number 15 is: A. 00001111 B. 0000110 C. 00001000 D. 0001100
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Answer

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Step 1:
I'll solve this decimal to binary conversion problem step by step:

Step 2:
: Understand Decimal to Binary Conversion

To convert a decimal number to binary, we divide the number repeatedly by 2 and track the remainders from bottom to top.

Step 3:
: Perform Decimal to Binary Conversion for 15

Let's divide 15 by 2 repeatedly: - 15 ÷ 2 = 7 remainder 1 - 7 ÷ 2 = 3 remainder 1 - 3 ÷ 2 = 1 remainder 1 - 1 ÷ 2 = 0 remainder 1

Step 4:
: Read Remainders from Bottom to Top

15_{10} = 1111_{2}
Reading the remainders from bottom to top gives us the binary representation:

Step 5:
: Verify the Binary Representation

1 \times 2^{3} + 1 \times 2^{2} + 1 \times 2^{1} + 1 \times 2^{0} = 8 + 4 + 2 + 1 = 15
Let's confirm by converting back:

Step 6:
: Add Leading Zeros to Make 8 -Bit Number

00001111_{2}

Final Answer

A. 00001111