Question

question 6
convert the following binary number (base 2) to octal (base 8).
111110011111₂ = (base 8)
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question 7

Explanation:

Step1: Group the binary digits

Starting from the right, group the binary digits \(111110011111_2\) into groups of three. Since \(111110011111\) has 12 digits, we can group them as \(111\ 110\ 011\ 111\).

Step2: Convert each group to octal

• For the group \(111_2\): \(1\times2^2 + 1\times2^1+1\times2^0=4 + 2+1 = 7\)
• For the group \(110_2\): \(1\times2^2+1\times2^1 + 0\times2^0=4+2+0 = 6\)
• For the group \(011_2\): \(0\times2^2+1\times2^1+1\times2^0=0 + 2+1=3\)
• For the group \(111_2\): \(1\times2^2 + 1\times2^1+1\times2^0=4 + 2+1 = 7\)

Answer:

\(7637_8\)