Binary to Octal Converter Calculator

A Binary to Octal Calculator is a specialized computational tool designed to convert numbers from the binary number system (base-2) to the octal number system (base-8).

Binary to Octal Calculator

Binary Number	Grouping	Octal Result
111000	111|000	70
101010101	101|010|101	525
11110000	011|110|000	360
10101111	010|101|111	257
11001100	011|001|100	314
100101	001|001|010	112
1101101	1|101|101	275
111111	000|111|111	77
1010001	001|010|001	121
0111100	00|111|100	74
00011011	000|110|11	33
01010101	010|101|01	125
1101001	1|101|001	651
10101	010 | 101	25
11011	011 | 011	33
1010111100	001 | 010 | 111 | 100	1274
01101010	001 | 101 | 010	152
11001	011 | 001	31
110110001010₂	110 | 110 | 001 | 010	6612

Binary to Octal Chart

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

Binary to Octal Conversion Formula

The formula involves:

• Grouping: Starting from the right, arrange binary digits in groups of three.
• Padding: Add leading zeros if necessary to complete the leftmost group.
• Conversion: Convert each group to its octal equivalent using the power series:
• For each group: (a × 2²) + (b × 2¹) + (c × 2⁰)

For example, converting 1101:

1101 → 001 | 101
001 → 1
101 → 5
Result: 15₈

How to Convert Binary to Octal?

Steps for Converting Binary to Octal

• Start from the right side of the binary number: 1010111₂
• Group the bits into sets of three: 1 010 111
• Add leading zeros to the leftmost group if needed: 001 010 111
• Convert each group of three bits to its octal equivalent:
  • 001 = 1
  • 010 = 2
  • 111 = 7

Therefore, 1010111₂ = 127₈

Binary to Octal Conversion Examples

Converting 10101 to Octal

Step-by-step process:

• Add leading zero: 010|101
• Convert groups:
  • 010 → 2
  • 101 → 5
• Result: 25₈

Converting 11011 to Octal

• Add leading zeros: 011|011
• Convert groups:
  • 011 → 3
  • 011 → 3
• Result: 33₈

Converting 1010111100 to Octal

• Group digits: 001|010|111|100
• Convert groups:
  • 001 → 1
  • 010 → 2
  • 111 → 7
  • 100 → 4
• Result: 1274₈

Converting 01101010 to Octal

• Group digits: 001|101|010
• Convert groups:
  • 001 → 1
  • 101 → 5
  • 010 → 2
• Result: 152₈

How to convert 10101 binary to octal?

Step 1: Starting from right, group digits in sets of 3

010 | 101

Step 2: Convert each group to decimal

010 = 2  
101 = 5

Step 3: Write the decimals from left to right: (10101)₂ = (25)₈

How to convert 11011 binary to octal?

Step 1: Group digits in sets of 3 from right

011 | 011

Step 2: Convert each group

011 = 3  
011 = 3

(11011)₂ = (33)₈

What is 1010111100 binary to octal?

Step 1: Group in sets of 3 from right

001 | 010 | 111 | 100

Step 2: Convert each group

001 = 1  
010 = 2  
111 = 7  
100 = 4

(1010111100)₂ = (1274)₈

How do you convert 01101010 binary to octal?

Step 1: Group in sets of 3

001 | 101 | 010

Step 2: Convert each group

001 = 1  
101 = 5  
010 = 2

(01101010)₂ = (152)₈

How to convert 11001 binary to octal?

Step 1: Group in sets of 3

011 | 001

Step 2: Convert each group

011 = 3  
001 = 1

(11001)₂ = (31)₈

How to convert 110110001010₂ binary to octal?

Step 1: Group in sets of 3

001 | 101 | 100 | 010 | 102

Note: The subscript “2” indicates it’s a binary number, not part of the digits.

Step 2: Convert each group

001 = 1  
101 = 5  
100 = 4  
010 = 2

(110110001010)₂ = (1542)₈

References

• IEEE Digital Library – Computer Arithmetic: https://ieeexplore.ieee.org/

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