Question

1) Перевести целые числа из десятичной системы счисления в троичную: 65, 325, 121. 2) Перевести целые числа из десятичной системы счисления в восьмеричную: 6435, 856 , 89, 998.

Answer 1

1) 65 = 2102
325 = 110001
121 = 11111

2) 6435 = 14443
856 = 1530
89 = 131
998 = 1746

Answer 2

Converting Decimal Numbers to Ternary (Base-3) System

To convert decimal numbers to the ternary system, we can use the method of successive division by the base (3) and noting the remainders. Let's convert the given decimal numbers to the ternary system:

1. 65 in decimal to ternary: - 65 divided by 3 equals 21 with a remainder of 2. - 21 divided by 3 equals 7 with a remainder of 0. - 7 divided by 3 equals 2 with a remainder of 1. - 2 divided by 3 equals 0 with a remainder of 2. - Reading the remainders from bottom to top, we get 2012 in ternary.

2. 325 in decimal to ternary: - 325 divided by 3 equals 108 with a remainder of 1. - 108 divided by 3 equals 36 with a remainder of 0. - 36 divided by 3 equals 12 with a remainder of 0. - 12 divided by 3 equals 4 with a remainder of 0. - 4 divided by 3 equals 1 with a remainder of 1. - 1 divided by 3 equals 0 with a remainder of 1. - Reading the remainders from bottom to top, we get 1001001 in ternary.

3. 121 in decimal to ternary: - 121 divided by 3 equals 40 with a remainder of 1. - 40 divided by 3 equals 13 with a remainder of 1. - 13 divided by 3 equals 4 with a remainder of 1. - 4 divided by 3 equals 1 with a remainder of 1. - 1 divided by 3 equals 0 with a remainder of 1. - Reading the remainders from bottom to top, we get 11111 in ternary.

Converting Decimal Numbers to Octal (Base-8) System

To convert decimal numbers to the octal system, we can use the method of successive division by the base (8) and noting the remainders. Let's convert the given decimal numbers to the octal system:

1. 6435 in decimal to octal: - 6435 divided by 8 equals 804 with a remainder of 3. - 804 divided by 8 equals 100 with a remainder of 4. - 100 divided by 8 equals 12 with a remainder of 4. - 12 divided by 8 equals 1 with a remainder of 4. - 1 divided by 8 equals 0 with a remainder of 1. - Reading the remainders from bottom to top, we get 14033 in octal.

2. 856 in decimal to octal: - 856 divided by 8 equals 107 with a remainder of 0. - 107 divided by 8 equals 13 with a remainder of 3. - 13 divided by 8 equals 1 with a remainder of 5. - 1 divided by 8 equals 0 with a remainder of 1. - Reading the remainders from bottom to top, we get 1530 in octal.

3. 89 in decimal to octal: - 89 divided by 8 equals 11 with a remainder of 1. - 11 divided by 8 equals 1 with a remainder of 3. - 1 divided by 8 equals 0 with a remainder of 1. - Reading the remainders from bottom to top, we get 131 in octal.

4. 998 in decimal to octal: - 998 divided by 8 equals 124 with a remainder of 6. - 124 divided by 8 equals 15 with a remainder of 4. - 15 divided by 8 equals 1 with a remainder of 7. - 1 divided by 8 equals 0 with a remainder of 1. - Reading the remainders from bottom to top, we get 1766 in octal.