Question 1. Convert octal 127 to hexadecimal.
Solution: 57
- Convert octal 127 to binary: 127 (octal) = 001 010 111 (binary).
- Group binary digits in sets of 4: 0001 0101 0111.
- Convert to hexadecimal: 0001 (1), 0101 (5), 0111 (7) = 57 (hex).
Question 2. Convert hexadecimal 9A to octal.
Solution: 232
- Convert hexadecimal 9A to binary: 9 = 1001, A = 1010.
- Group binary digits in sets of 3: 001 001 101 010.
- Convert to octal: 001 (1), 001 (1), 101 (5), 010 (2) = 232 (octal).
Question 3. Convert octal 156 to hexadecimal.
Solution: 6E
- Convert octal 156 to binary: 156 (octal) = 001 101 110 (binary).
- Group binary digits in sets of 4: 0001 1011 0110.
- Convert to hexadecimal: 0001 (1), 1011 (B), 0110 (6) = 6E (hex).
Question 4. Convert hexadecimal 1D7 to octal.
Solution: 727
- Convert hexadecimal 1D7 to binary: 1 = 0001, D = 1101, 7 = 0111.
- Group binary digits in sets of 3: 001 101 110 111.
- Convert to octal: 001 (1), 101 (5), 110 (6), 111 (7) = 727 (octal).
Question 5. Convert octal 241 to hexadecimal.
Solution: A1
- Convert octal 241 to binary: 241 (octal) = 010 100 001 (binary).
- Group binary digits in sets of 4: 0010 1000 0001.
- Convert to hexadecimal: 0010 (2), 1000 (A), 0001 (1) = A1 (hex).
Question 6. Convert hexadecimal 22F to octal.
Solution: 1077
- Convert hexadecimal 22F to binary: 2 = 0010, 2 = 0010, F = 1111.
- Group binary digits in sets of 3: 001 000 100 111 111.
- Convert to octal: 001 (1), 000 (0), 100 (4), 111 (7), 111 (7) = 1077 (octal).
Question 7. Convert octal 302 to hexadecimal.
Solution: C2
- Convert octal 302 to binary: 302 (octal) = 011 000 010 (binary).
- Group binary digits in sets of 4: 0011 0000 0010.
- Convert to hexadecimal: 0011 (3), 0000 (0), 0010 (2) = C2 (hex).
Question 8. Convert hexadecimal 15A to octal.
Solution: 532
- Convert hexadecimal 15A to binary: 1 = 0001, 5 = 0101, A = 1010.
- Group binary digits in sets of 3: 000 101 101 010.
- Convert to octal: 000 (0), 101 (5), 101 (5), 010 (2) = 532 (octal).
Question 9. Convert octal 456 to hexadecimal.
Solution: 12E
- Convert octal 456 to binary: 456 (octal) = 100 101 110 (binary).
- Group binary digits in sets of 4: 0001 0010 1110.
- Convert to hexadecimal: 0001 (1), 0010 (2), 1110 (E) = 12E (hex).
Question 10. Convert hexadecimal 37F to octal.
Solution: 1777
- Convert hexadecimal 37F to binary: 3 = 0011, 7 = 0111, F = 1111.
- Group binary digits in sets of 3: 001 101 111 111 111.
- Convert to octal: 001 (1), 101 (5), 111 (7), 111 (7), 111 (7) = 1777 (octal).
Question 11. Convert octal 643 to hexadecimal.
Solution: 143
- Convert octal 643 to binary: 643 (octal) = 110 100 011 (binary).
- Group binary digits in sets of 4: 0110 1000 0011.
- Convert to hexadecimal: 0110 (6), 1000 (8), 0011 (3) = 143 (hex).