1. Stating the problem: Convert the given hexadecimal numbers A9, E7, 6E, 1F, and 2A to their equivalent octal values. 2. Recall that to convert from hexadecimal (base 16) to octal (base 8) easily, first convert hexadecimal to binary (base 2), then group the binary digits into groups of three (starting from the right) to convert to octal. 3. Convert each hexadecimal digit to 4-bit binary: - A9: A = 1010, 9 = 1001 so A9 = 10101001 - E7: E = 1110, 7 = 0111 so E7 = 11100111 - 6E: 6 = 0110, E = 1110 so 6E = 01101110 - 1F: 1 = 0001, F = 1111 so 1F = 00011111 - 2A: 2 = 0010, A = 1010 so 2A = 00101010 4. Group each binary string into groups of three from the right: - A9: 10 101 001 → pad left with one zero to make a full group of 3: 010 101 001 - E7: 111 001 111 - 6E: 011 011 110 - 1F: 000 111 111 - 2A: 001 010 101 0 → pad left with two zeros to make groups of 3: 000 101 010 (Note: For A9, third digit padded) 5. Convert each 3-bit group to octal digit: - A9: 010=2, 101=5, 001=1 so octal is 251 - E7: 111=7, 001=1, 111=7 so octal is 717 - 6E: 011=3, 011=3, 110=6 so octal is 336 - 1F: 000=0, 111=7, 111=7 so octal is 077 or just 77 - 2A: 000=0, 101=5, 010=2 so octal is 052 or just 52 6. Final answers: - Hex A9 = Octal 251 - Hex E7 = Octal 717 - Hex 6E = Octal 336 - Hex 1F = Octal 77 - Hex 2A = Octal 52 These conversions show each step clearly from hex to binary to octal.