Octal and hexadecimal are both number systems used frequently in computing and digital electronics.
Octal: Base-8 (digits 0–7)
Hexadecimal: Base-16 (digits 0–9 and letters A–F)
Direct conversion from octal to hexadecimal isn’t as straightforward as decimal conversions, so we typically use an intermediate step.
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There are two main ways to convert octal numbers into hexadecima
Octal → Binary → Hexadecimal
Why this works:
Every octal digit can be represented by 3 binary digits.
Every hexadecimal digit can be represented by 4 binary digits.
So we can use binary as a bridge.
Convert each octal digit to a 3-bit binary value
7 → 111
2 → 010
So, (72)₈ = 111010₂
Group the binary number into 4-bit chunks (from right to left)
111010 → 0001 11010 → Add a leading zero to make 4 bits: 0011 1010
But cleaner:
(111010)₂ → group as: 0111 010
Now we add a leading zero: 0011 1010 → This becomes:(0111 0010)₂ = (7 2)₁₆
Oops! That’s incorrect. Let's fix the grouping:
(111010)₂ = 0001 1101 0 → still doesn’t group cleanly.
Better grouping:
From right to left:111010 → 11 1010 → add 2 leading zeros → 0011 1010
→ 0011 (3), 1010 (A)
Final Answer:
(72)₈ = (3A)₁₆
Convert (145)₈ to hexadecimal
Octal digits → Binary:
1 → 001
4 → 100
5 → 101
(145)₈ = (001 100 101)₂ = 001100101₂
Group from right:
= 0001 1001 01 → add leading zeros → 0001 1001 0100 (12 bits)
Group as: 0001 1001 0101 →
= (1)(9)(5) → (195)₁₆
Octal → Decimal → Hexadecimal
Why this works:
Convert from base-8 to base-10 (decimal) using positional values
Then convert decimal to base-16
Each digit is multiplied by powers of 8:
= 7 × 8¹ + 5 × 8⁰
= 7 × 8 + 5 × 1
= 56 + 5 = 61₁₀
Step 2: Convert 61₁₀ to Hexadecimal
Divide by 16:
16 | 61
----
16 | 3 → remainder: 13
→ remainder: 13 = D in hex(61)₁₀ = (3D)₁₆Convert (316)₈ to hexadecimal
Step 1: Convert to Decimal
= 3 × 8² + 1 × 8¹ + 6 × 8⁰
= 3 × 64 + 1 × 8 + 6 × 1
= 192 + 8 + 6 = 206₁₀
Step 2: Convert 206 to Hexadecimal
16 | 206
-----
16 | 12 → remainder 14 → E
→ 12 = C(316)₈ = (CE)₁₆Summary of Steps
| Method | Steps |
|---|---|
| Method 1 | Octal → Binary → Hexadecimal |
| Method 2 | Octal → Decimal → Hexadecimal |
Practice Examples
Try converting these octal numbers to hexadecimal:
- (104)₈ = ?
- (241)₈ = ?
- (377)₈ = ?
- (25)₈ = ?
FAQs
Q: Do I always have to go through binary or decimal?
Yes, because there's no direct formula for converting octal to hexadecimal. Binary or decimal acts as a helpful bridge.
Q: Which method is easier?
If you're good with binary, Method 1 is faster.
If you're comfortable with arithmetic, Method 2 may feel easier.