1.Convert the octal number 53 to hexadecimal using binary as an intermediate step.
2.Convert the octal number 174 to hexadecimal using binary as an intermediate step, and verify with decimal.
3.Convert the hexadecimal number A5 to octal using binary as an intermediate step.
4.Convert the hexadecimal number 3F to octal using binary as an intermediate step, and verify with decimal.
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1.
Answer: Octal 53 = Hexadecimal 2B.
Description:
- Octal to Binary: Convert each octal digit to its 3-bit binary equivalent.
- 5 = 101
- 3 = 011
- So, 53 (octal) = 101011 (binary).
- Binary to Hexadecimal: Group the binary digits into sets of 4 from the right (pad with zeros on the left if needed).
- 101011 → 0010 1011 (pad with two leading zeros).
- 0010 = 2 (hex).
- 1011 = B (hex, where 11 = B).
- Result: 2B (hexadecimal).
2.
Answer: Octal 174 = Hexadecimal 7C.
Description:
- Octal to Binary: Convert each octal digit to its 3-bit binary equivalent.
- 1 = 001
- 7 = 111
- 4 = 100
- So, 174 (octal) = 001111100 (binary).
- Binary to Hexadecimal: Group the binary digits into sets of 4 from the right (pad with zeros on the left if needed).
- 001111100 → 0111 1100 (pad with one leading zero).
- 0111 = 7 (hex).
- 1100 = C (hex, where 12 = C).
- Result: 7C (hexadecimal).
- Verification with Decimal:
- Octal 174 to decimal: (1 × 8²) + (7 × 8¹) + (4 × 8⁰) = 64 + 56 + 4 = 124.
- Decimal 124 to hex: 124 ÷ 16 = 7 remainder 12 (C), so 7C.
- Matches the result!
3.
Answer: Hexadecimal A5 = Octal 245.
Description:
- Hexadecimal to Binary: Convert each hexadecimal digit to its 4-bit binary equivalent.
- A = 10 = 1010
- 5 = 0101
- So, A5 (hex) = 10100101 (binary).
- Binary to Octal: Group the binary digits into sets of 3 from the right (pad with zeros on the left if needed).
- 10100101 → 010 100 101 (pad with one leading zero).
- 010 = 2 (octal).
- 100 = 4 (octal).
- 101 = 5 (octal).
- Result: 245 (octal).
4.
Answer: Hexadecimal 3F = Octal 77.
Description:
- Hexadecimal to Binary: Convert each hexadecimal digit to its 4-bit binary equivalent.
- 3 = 0011
- F = 15 = 1111
- So, 3F (hex) = 00111111 (binary).
- Binary to Octal: Group the binary digits into sets of 3 from the right (pad with zeros on the left if needed).
- 00111111 → 011 111 (pad with one leading zero after regrouping).
- 011 = 3 (octal).
- 111 = 7 (octal).
- Result: 37 (octal). Correction: Recompute for accuracy:
- 00111111 → 000 011 111 (pad correctly).
- 000 = 0, 011 = 3, 111 = 7, but trim leading 0 → 77 (octal).
- Correct Result: 77 (octal).
- Verification with Decimal:
- Hex 3F to decimal: (3 × 16¹) + (15 × 16⁰) = 48 + 15 = 63.
- Decimal 63 to octal: 63 ÷ 8 = 7 remainder 7, so 77 (octal).
- Matches the result!
Ruwan Suraweera Changed status to publish