Question

I) 0xBED into 3-base representation
ii) 3217 into 2-base (binary) representation

Answer 1

Answer #1

(11012002)3

step by step Explanation

OxBED

in hexadecimal

we can write these as

A=10

B=11

C=12

D=13

E=14

=(13*
`16^(0)`)+(14*
`16^(1)`)+(11*
`16^(0)`)

=13+224+2816=3050

Now we will divide this number by 3 and take reminder aside

to convert it into base 3

Number Reminder

3053 2

1017 0

339 0

113 2

37 1

12 0

4 1

1 1

hence number will be

(11012002)3

Answer #2

(110010010001)2

Step-by-step explanation

we can onvert 3217 into base 2 by dividing it by 2

and take reminder of the number aside in every step

Number Reminder

3217 1

1608 0

804 0

402 0

201 1

100 0

50 0

25 1

12 0

6 0

3 1

1 1

The number will be

(110010010001)2

Answer 2

i. 0xBED is a hexadecimal therefore we need to convert it to decimal first for ease of conversion. The calculation would just need B = 11, E = 14, and D = 13.


`13+(14*16)+(11* 16^(2))=3,053`

Then we just continuously divide the number by 3 and take the remainder in each step.

NUMBER REMAINDER
3053 2
1017 0
339 0
113 2
37 1
12 0
4 1
1 1
0

Finally we read the remainders from bottom to top to get the number's base 3 representation.

ANSWER: 11012002 (base 3)

ii. We can easily convert the decimal 3217 to binary by continuously dividing the number by 2 and taking the remainder in each step.

NUMBER REMAINDER
3217 1
1608 0
804 0
402 0
201 1
100 0
50 0
25 1
12 0
6 0
3 1
1 1
0

Then, we just read the remainder from bottom to top to get the decimal's binary representation.

ANSWER: 110010010001 (base 2)