What is 101010 binary in octal?

Grouping 101010 into sets of three bits starting from the right gives 101 and 010. The binary 101 is octal 5, and 010 is octal 2. Summing them together yields 52 in octal.

Mathematical Tutorial

How to Convert Binary to Octal

Learn how to group binary digits into sets of three to compute octal values, along with examples for fractional binary numbers.

Try it: Binary to Octal mini-calculator

Octal Result: 326

The grouping method.

Octal is a base-8 number system, which means it uses 8 unique symbols (0-7). Because 2³ = 8, exactly **three binary digits** (bits) map to **one octal digit**.

This makes converting binary to octal extremely simple: you do not need to perform complex division. Instead, you simply group the binary string into sets of three starting from the right.

Binary to octal steps by hand.

Start with the binary number (e.g., 11010110).
Separate the bits into groups of three, starting from the rightmost bit. If the leftmost group has fewer than three bits, pad it with leading zeros:
11010110 ➔ [011] [010] [110]
Convert each 3-bit binary group into its decimal equivalent (since values range from 0 to 7):
- 011 = 0 · 4 + 1 · 2 + 1 · 1 = 3
- 010 = 0 · 4 + 1 · 2 + 0 · 1 = 2
- 110 = 1 · 4 + 1 · 2 + 0 · 1 = 6
Concatenate the results to get the octal representation: 326.

Fractional binary to octal.

For binary numbers containing a binary point (fractional binary), separate the groupings in both directions starting from the decimal point:

Example: Convert 11010111.010110 to octal:

• Left of decimal point (group right-to-left): [011] [010] [111] ➔ 327₈

• Right of decimal point (group left-to-right): [010] [110] ➔ 26₈

• Result: 327.26₈

Frequently Asked Questions

How do you convert binary to octal? ▼

To convert binary to octal, group the binary bits into sets of three, starting from the rightmost digit. Pad the leftmost group with leading zeros if it has fewer than three bits. Convert each 3-bit group into its equivalent octal digit (0 to 7).

What is the octal value of binary 10101? ▼

The binary number 10101 is equal to 25 in octal. Calculation: Group the bits into [010] [101]. Converting each group gives 2 and 5, yielding 25₈.

Why do we group bits into sets of three for octal conversion? ▼

Since the octal system is base-8 and 8 is a power of 2 (specifically 2³), exactly three binary bits are needed to uniquely represent all 8 possible octal digits (0 through 7).

Binary to Octal Table

Binary	Octal
000	0
001	1
010	2
011	3
100	4
101	5
110	6
111	7