What is the octal equivalent of the binary number:10111101ans.275675573572 Previous Marked for Review Next

1. Break Down the Problem

To convert the binary number $10111101$ to its octal equivalent, we need to group the binary digits in sets of three, starting from the right. If there are not enough digits on the left, we can add leading zeros.

2. Relevant Concepts

The binary system is base-2, and the octal system is base-8. Each octal digit corresponds to three binary digits (since $2^3 = 8$). Therefore, we will convert the binary number directly to octal by converting each group of three binary digits to a single octal digit.

3. Analysis and Detail

• The binary number: $10111101$

• Grouping the digits in sets of three (from right):

  $1 011 110$

  Adding leading zeros:

  $001 011 110$

• Now, convert each group of three binary digits to its octal equivalent:

  • $001$ in binary = $1$ in octal
  • $011$ in binary = $3$ in octal
  • $110$ in binary = $6$ in octal

4. Verify and Summarize

Combining the octal digits obtained from the groups, we have:

$1 \ 3 \ 6$

Thus, the octal equivalent of the binary number $10111101$ is $136$.

Final Answer

The octal equivalent of the binary number $10111101$ is $136$.