Question

Convert the binary (base-2) number 1001 to decimal (base-10).

Answer 1

Answer:

Binary 1001 is decimal 9.

Explanation:

For this problem, we simply need to understand that a binary number can be converted to a decimal number with multiplication of the "on bits".  Let's begin.

First, note that in binary, as digits grow to the right, they are being multiplied by 2.  In decimal, as digits grow to the right, they are being multiplied by 10.

For example

0001 in binary is equivalent to 2^0 since a 1 is in the first position.

1 in decimal is equivalent to 10^0 since it is in the first position.

Taking this concept a bit further consider:

101 in binary is equivalent to 2^2 + 2^0 since a 1 is in the third position and a 1 is in the first position.

101 in decimal is equivalent to 10^2 + 10^0 since a value is in the third position and a value is also in the first position.

With this in mind, let's convert the binary 1001 to decimal.

1001

= 1 * 2^3 + 0 * 2^2 + 0 * 2^1 + 1 * 2^0

= 2^3 + 2^0

= 8 + 1

= 9

Hence, binary 1001 is decimal 9.

Cheers.

Answer 2

By converting the binary number $(1001)_2$ to decimal, we get $(9)_{10}$. A complete description is provided below.

The given binary number is:

• (1001)₂

To convert binary to decimal, we have to do is:

= $1 \ 0 \ 0 \ 1$

= $2^3\times 2^2\times 2^1\times 2^0$

= $1\times 2^3 + 0\times 2^2 + 0\times 2^1 + 1\times 2^0$

= $8+0+0+1$

= $9$

or,

= $(9)_{10}$

Thus the answer above is appropriate.

Learn more about binary number here:

https://brainly.com/question/12846179