Convert decimal number 81 and 124 into binary, octal and hexadecimal number system?
The correct answer and explanation is:
Let’s convert the decimal numbers 81 and 124 into binary, octal, and hexadecimal number systems, and then provide an explanation.
✅ Conversions
🔹 Decimal 81:
- Binary: 81 ÷ 2 =
1010001 - Octal: 81 ÷ 8 =
121 - Hexadecimal: 81 ÷ 16 =
51(since 5×16 + 1 = 81)
🔹 Decimal 124:
- Binary: 124 ÷ 2 =
1111100 - Octal: 124 ÷ 8 =
174 - Hexadecimal: 124 ÷ 16 =
7C(since 7×16 + 12 = 124, and 12 = C in hex)
✅ Summary Table
| Decimal | Binary | Octal | Hexadecimal |
|---|---|---|---|
| 81 | 1010001 | 121 | 51 |
| 124 | 1111100 | 174 | 7C |
🧠 Explanation (300 words)
Number systems are different ways to represent numbers using various bases. The decimal system is base-10, the most common in everyday life, using digits 0–9. However, computers use binary (base-2) because they operate with two states: ON and OFF, represented by 1 and 0.
To convert decimal to binary, divide the number by 2 repeatedly and record the remainders. Reading the remainders from bottom to top gives the binary number.
For example:
- 81 → Binary:
- 81 ÷ 2 = 40, remainder 1
- 40 ÷ 2 = 20, remainder 0
- 20 ÷ 2 = 10, remainder 0
- 10 ÷ 2 = 5, remainder 0
- 5 ÷ 2 = 2, remainder 1
- 2 ÷ 2 = 1, remainder 0
- 1 ÷ 2 = 0, remainder 1
⇒ 1010001
Octal (base-8) uses digits 0–7. Group binary digits in 3s (from right), then convert to octal. For 81:
- Binary:
1010001→ Pad to 8 bits:01010001 - Groups:
010 100 001→ 2 4 1 → Octal = 121
Hexadecimal (base-16) uses 0–9 and A–F (where A = 10 to F = 15). Group binary digits in 4s:
- Binary of 81:
01010001→ Groups:0101 0001→ 5 and 1 → Hex = 51
These conversions are essential in computing, as binary is used for logic, octal and hex for simplifying binary representation in programming and hardware.