Question

question 18

convert binary 1111101 to octal.

95₈
275₈
175₈
761₈

Explanation:

Step1: Group the binary digits

Group the binary number \(1111101\) from right - to - left in groups of 3. Since the left - most group may have less than 3 digits, we can add leading zeros.
The binary number \(1111101\) can be written as \(001\ 111\ 101\)

Step2: Convert each group to decimal

• For the group \(001\): \(0\times2^{2}+0\times2^{1}+1\times2^{0}=1\)
• For the group \(111\): \(1\times2^{2}+1\times2^{1}+1\times2^{0}=4 + 2+1=7\)
• For the group \(101\): \(1\times2^{2}+0\times2^{1}+1\times2^{0}=4+0 + 1=5\)

Step3: Combine the decimal values

Combining the decimal values of each group, we get the octal number \(175_{8}\)

Answer:

C. \(175_{8}\)