The octal equivalent of the binary number 1011101011 is

Concept: Binary uses base 2 and octal uses base 8, and 8 = 2³. So exactly three binary bits encode one octal digit (values 0 to 7). To convert binary to octal, partition the bits into groups of three starting from the rightmost (least significant) bit, padding the leftmost group with leading zeros, then replace each 3-bit group by the octal digit it represents.

Application: The 10-bit number 1011101011 is grouped from the right and the top group is padded to three bits:

1. Group from the right into threes: 1 | 011 | 101 | 011.

2. Pad the leftmost group with leading zeros: 001 | 011 | 101 | 011.

3. Convert 001 = 0·4 + 0·2 + 1·1 = 1.

4. Convert 011 = 0·4 + 1·2 + 1·1 = 3.

5. Convert 101 = 1·4 + 0·2 + 1·1 = 5.

6. Convert 011 = 0·4 + 1·2 + 1·1 = 3.

7. Read the octal digits in order: 1, 3, 5, 3, giving 1353.

Cross-check: Convert through decimal as an independent route. 1011101011 in binary equals 512 + 128 + 64 + 32 + 8 + 2 + 1 = 747 in decimal. Dividing 747 by 8 repeatedly gives remainders 3, 5, 3, 1 (read upward) = 1353 in octal, which matches.

Therefore the octal equivalent is 1353.