3 2.44 12 3 - Add, subtract, and multiply in binary: (a) 110 and 1010 (b) 111101

Question

3

2.44

12

3

-

Add, subtract, and multiply in binary:

(a)

110 and 1010

(b)

111101 and 10111

(c)

111001 and 10110

4

-

Convert to octal. Convert to hexadecimal. Then convert both of your answer to decimal, and

verify that they are the same:

(a)

111110101001.101

2

(b)

100111001111.10

2

5

-

Devise a scheme for converting base 3 numbers directly to base9. Use your method to convert

the

following number to base 9:

1010221.10202

3

2- Convert to base 5: 3B2.4412 3- Add, subtract, and multiply in binary: (a) 110 and 1010 (b) 111101 and 10111 (c) 111001 and 10110 Convert to octal. Convert to hexadecimal. Then convert both of your answer to decimal, and verify that they are the same: 4- (b) 100111001111.102 Devise a scheme for converting base 3 numbers directly to base9. Use your method to convert the following number to base 9: 5- 1010221.102023

Explanation / Answer

I am solving the first question, Question2 in this case as per Chegg guidelines, post multiple question to get the remaining answers

Q2)

3B2.44

Number in Decimal = 3 * (12)^2 + 11 * 12 + 2 * 12^0 + 4 * (12)^(-1) + 4 * (12)^(-2)

=> 566.361111

Dividing the number with 5^3, first we get 4

Remainder is equal to 66, dividing it by 5^2, we get 2

Remainder is 16, dividing it 5, we get 3

Remainder is 1, dividiing it 5^0, we get

Hence, the number without decimal will be 4231

For calculating the decimal part

0.3611 = 1 * 5^(-1) + 0.1611
0.1611 = 4 * 5^(-2) + 0.011
0.011 = 1 * 5^(-3) + 0.003
0.003 = 1 * 5^(-4) + 0.0014

we get the answer 1 * 5^(-1) + 4 * 5^(-2) + 1 * 5^(-3) + 1 * 5^(-4)

Hence the final answer in two decimal places will be 4231.14 and in four decimal places will be 4231.1411

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