Respuesta :

fieryanswererft

Answer:

[tex]\large{\boxed{35_{10} = \sf 23_{16}}}[/tex]

Explanation:

[tex]\sf Given : 35_{10}[/tex]

Compute:

35 ÷ 16 = 2.1875 = 2R3

2 ÷ 16 = 0.125 = 0R2

Jot down the remainders:

  • 3        ↑
  • 2        ↑

======

[tex]\sf Answer : \ 35_{10} = 23_{16}[/tex]

[tex]\hrulefill[/tex]

Let's look at another example:  [tex]\sf 325_{10} = [?]_{16}[/tex]

Compute:

325 ÷ 16 = 20.3125 = 20R5

20 ÷ 16 = 1.25 = 1R4

1 ÷ 16 = 0.0625 = 0R1

Jot down remainders:

  • 5        ↑
  • 4        ↑
  • 1         ↑

=====

[tex]\sf 325_{10} = [145]_{16}[/tex]

[tex]\hrulefill[/tex]

Another example: [tex]\sf 500_{10} = [?]_{15}[/tex]

Compute:

500 ÷ 15 = 33.33... = 33R5

33 ÷ 15 = 2.2 = 2R3

2 ÷ 15 = 0.13... = 0R2

Jot down remainders:

  • 5      ↑
  • 3       ↑
  • 2       ↑

=====

[tex]\sf 500_{10} = [235]_{15}[/tex]

This is general conversation of decimal integer to hexadecimal integer

Let's check

  • (35)_10

This is in decimal form

We know the ways to convert decimal into other forms like

  • Binary—»Divide by 2
  • Octal—»Divide by 8
  • Hexadecimal —»Divide by 16

For third way

  • 35/16=2

(2)_16 is one part

Next

  • 35%16=3

3 is not divisible by 16

i.e

  • 3%16=0

Hence

other part is (3)_16

Add (not general addition)

The final answer is

  • (23)_16

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