How to convert decimal to binary, without computer or scientific calculator?

Question

What is the easiest way to convert binary to decimal, but not like this method:

2)156 0

2)78 0

2)39 1

2)19 1

2)9 1

2)4 0

2)2 0

1

please don't use a computer or scientific calculator.

Answer 1

Ok this is actually very easy.

For the one digit you mulitiply it by two to the zero power which is 1.

For the tens digit you multiply it by two to the first power which is 2.

For the hundreds digit you multiply it by two to the second power which is 4.

For the thousands digit you multiply it by two to the third power which is 8.

So on and so on, you get the picture.

When you're done add it all up and that is your answer in decimal for also known as base 10.

Answer 2

Sorry, but the easiest way is just something similar to the opposite of what you have:

0 * 2^0 (AKA 1) = 0

0 * 2^1 (AKA 2) = 0

1 * 2^2 (AKA 4) = 4

1 * 2^3 (AKA 8) = 8

1 * 2^4 (AKA 16) = 16

0 * 2^5 (AKA 32) = 0

0 * 2^5 (AKA 64) = 0

1 * 2^6 (AKA 128) = 128

--------------------------------------

============== 156

Answer 3

There are two basic ways.

The method you rejected in your question is the better of the two.

The other method is as follows:

Find largest power of two and note down.

Subtract it from the number and repeat

until you reach 0.

2^7 < 156 < 2^8 --> 1 x 2^7

156 - 128 = 28

28 < 2^6 --> 0 x 2^6

28 < 2^5 --> 0 x 2^5

2^4 < 28 < 2^5 --> 1 x 2^4

28 - 16 = 12

2^3 < 12 < 2^4 --> 1 x 2^3

12 - 8 = 4

2^2 = 4 --> 1 x 2^2 +

4 - 4 = 0

done:

10011100

Take your pick.

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