Question

Devise a scheme for converting base 3 numbers directly to base9. Use your method to convert the following number to base 9: 5- 11022.22013 6- Add, subtract, and multiply in binary: (a) 1111 and 1101 (b) 1101101 and 11110

Answer 1

To convert 11022.22013 from base 3 to base 9, you can use the expansion method by multiplying the digits with increasing powers of 3 and then adding them up. In binary (base 2), addition, subtraction, and multiplication can be performed similarly to decimal (base 10).

Step-by-step explanation:

To convert a base 3 number directly to base 9, we can use the expansion method by multiplying the digits with increasing powers of 3 and then adding them up. For example, to convert 11022.22013 from base 3 to base 9:

1. 5 × 34 = 405
2. 1 × 33 = 27
3. 0 × 32 = 0
4. 2 × 31 = 6
5. 2 × 30 = 2
6. 2 × 3-1 = 6/9
7. 2 × 3-2 = 2/27
8. 0 × 3-3 = 0
9. 1 × 3-4 = 1/81
10. 3 × 3-5 = 3/243

Adding up all the digits, we get 405 + 27 + 0 + 6 + 2 + 6/9 + 2/27 + 0 + 1/81 + 3/243, which simplifies to 432.36906 in base 9.

In binary (base 2), addition, subtraction, and multiplication can be performed in a similar way as in decimal (base 10). For example, (a) 1111 + 1101 = 11000, and (b) 1101101 × 11110 = 11000111010.