Q
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
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