Number System ArithmeticFree Interactive Tool

Octal Calculator

All-in-one octal calculator for addition, subtraction, multiplication, and division in base 8. Designed for software developers, electrical engineers, students, and computer architecture researchers requiring deterministic client-side accuracy.

Engine: Client-Side Verified (0ms Latency)

Operation

First Octal Number (A)

Enter octal digits (0 through 7).

Second Octal Number (B)

Calculated Output

Primary Representation

Calculating...

Step-by-Step Mathematical Proof

Active Derivation

Ready. Enter input above to generate derivation.

Concept

What Is Octal Calculator?

The Octal Calculator performs all four fundamental arithmetic operations directly in base 8, managing carries and borrows modulo 8.

Methodology

How Does It Work?

Columns wrap at 8 rather than 10. For addition, sum >= 8 produces a carry. For subtraction, borrowing yields 8.

Formula & Rules

Mathematical Algorithm

A_8 \odot B_8 = R_8 \quad (\odot \in \{+, -, \times, \div\})

Worked Problem

Step-by-Step Example

75_8 (61) + 34_8 (28) = 131_8 (89 in decimal).

Important Rules & Edge Cases

Digits 0 through 7 only.

Practical Applications in Engineering

Unix permission calculations.
Telecommunications firmware verification.

Common Mistakes to Avoid

Caution: Carrying at 10 instead of 8.

FAQ

Frequently Asked Questions

What is 7 + 7 in octal?

7 + 7 = 14 in decimal = 16 in octal (1×8 + 6 = 14).

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