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katovenus [111]
4 years ago
9

Convert the following: 110110two to base ten 25ten to base two​

Mathematics
1 answer:
blagie [28]4 years ago
7 0

Answer:

  • 110110 in base 2 when converted in base 10 will be equal to 54
  • 25 in base 10 is equal to 1001 base 2

Step-by-step explanation:

Part 1: 110110two to base ten

For conversion from base 2 to base 10 we multiply each digits of given number with powers of 2

So

=1*2^5 + 1 * 2^4 + 0 * 2^3 + 1 *2^2 + 1* 2^1 + 0*2^0\\ =1*32+ 1* 16 + 0 + 1*4 + 1*2 +0\\ =32 + 16 +4 + 2\\ = 54

So 110110two when converted in base 10 will be equal to 54

Part 2: 25ten to base two

For conversion from base 10 to base 2 we will divide the given number with 2 repeatedly and store the remainders until the quotient comes 1. The solution is as follows:

25/2 = 12     remainder 1

12/2 = 6       remainder 0

6/2 = 3        remainder 0

3/2 = 1         remainder 1

Now the remainders will be written in inverse order as:

=1001 base 2

So 25 in base 10 is equal to 1001 base 2

I hope it will help you!

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General Formulas and Concepts:

<u>Pre-Algebra</u>

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Step-by-step explanation:

<u>Step 1: Define equation</u>

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<u>Step 2: Solve for </u><em><u>x</u></em>

  1. Distribute:                                   5x + 20 = 8 + 2x + 3
  2. Combine like terms:                   5x + 20 = 2x + 11
  3. Subtract 2x on both sides:        3x + 20 = 11
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<u>Step 3: Check</u>

<em>Plug in x to verify it's a solution.</em>

  1. Substitute:                    5(-3 + 4) = -2(-4 - -3) + 3
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  5. Add:                              5 = 5

Here we see that 5 does indeed equal 5. ∴ x = -3 is a solution of the equation.

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