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3 years ago

Convert the following decimal numbers into (a) binary and (b) hexadecimal forms.a. 25 b. 250c. 2500 d. 25555

Computers and Technology

1 answer:

musickatia [10]3 years ago

4 0

Answer:

Binary :

11001 base 2

11111010 base 2

100111000100 base 2

110001111010011 base 2

Hexadecimal:

19 base 16

FA base 16

9C4 base 16

63D3 base 16

Explanation:

For hexadecimal :

10 = A

11 = B

12 = C

13 = D

14 = E

15 = F

1.)

25 decimal :

To binary : ; Divide 25 by 2, for each division, the remainder is the binary value :

Divide by 2 _ Quotient __ binary value

25 ÷ 2 _______ 12 ______ 1

12 ÷ 2 _______ 6 ______ 0

6 ÷ 2 ________3 ______ 0

3 ÷ 2 ________ 1 ______ 1

1 ÷ 2 ________ 0 ______ 1

From bottom to top : 11001 base 2

25 decimal To hexadecimal

Divide by 16 _ Quotient __ hexadecimal value

25 ÷ 16 _______ 1 ______ 9

1 ÷ 16 _______ 0 ______ 1

25 base 10 = 19 base 16

2.)

250 decimal to binary :

Divide by 2 _ Quotient __ binary value

250 ÷ 2 _____ 125 ______ 0

125 ÷ 2 ______ 62 ______ 1

62 ÷ 2 _______ 31 ______ 0

31 ÷ 2 ________15 ______ 1

15 ÷ 2 ________ 7 ______ 1

7 ÷ 2 ________ 3 _______ 1

3 ÷ 2 ________ 1 ________ 1

1 ÷ 2 ________ 0 ________ 1

250 base 10 = 11111010 base 2

250 base 10 to base 16:

Divide by 16 _ Quotient __ hexadecimal value

250 ÷ 16 _______ 15 ______ 10

15 ÷ 16 _______ 0 _________ 15

250 base 10 = FA base 16

3.)

2500 decimal to binary :

Divide by 2 _ Quotient __ binary value

2500 ÷ 2 _____ 1250 ______ 0

1250 ÷ 2 ______ 625 ______ 0

625 ÷ 2 _______ 312 ______ 1

312 ÷ 2 ________156 ______ 0

156 ÷ 2 ________ 78 ______ 0

78 ÷ 2 ________ 39 _______ 0

39 ÷ 2 ________ 19 ________ 1

19 ÷ 2 _________9 ________ 1

9 ÷ 2 _________4 _________1

4 ÷ 2 _________ 2 ________ 0

2 ÷ 2 _________ 1 _________0

1 ÷ 2 _________ 0 _________ 1

2500 decimal = 100111000100 base 2

2500 base 10 to hexadecimal :

Divide by 16 _ Quotient __ hexadecimal value

2500 ÷ 16 _______ 156 ______ 4

156 ÷ 16 __________ 9 _______12

9 ÷ 16 ___________ 0 _______ 9

2500 base 10 = 9C4 base 16

4.)

25555 base ten to base 2 :

Divide by 2 _ Quotient __ binary value

25555 ÷ 2 ____ 12777 ______ 1

12777 ÷ 2 _____ 6388 _____ 1

6388 ÷ 2 ______3194 ______ 0

3194 ÷ 2 ______1597 ______ 0

1597 ÷ 2 ______ 798______ 1

798 ÷ 2 ______ 399_______ 0

399 ÷ 2 ______ 199________ 1

199 ÷ 2 _______99 ________ 1

99 ÷ 2 _______49 _________1

49 ÷ 2 _______24 ________ 1

24 ÷ 2 _______12_________0

12 ÷ 2 ________6 _________ 0

6 ÷ 2 _________3 ________0

3 ÷2 _________ 1 _________ 1

1 ÷ 2 _________0 _________ 1

25555 base 10 = 110001111010011 base 2

25555 base 10 to hexadecimal :

Divide by 16 _ Quotient __ hexadecimal value

25555 ÷ 16 __ 1597 ______ 3

1597 ÷ 16 _____ 99______ 13

99 ÷ 16 ________ 6 _______ 3

6 ÷ 16 _________ 0 ______ 6

25555 base 10 = 63D3 base 16

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