Question

Convert each of the following binary representations to its equivalent base 10 form
I. 0101
Ii. 1001
Iii. 1 011
Iv.0110
V.10000

Answer 1

Answer:

1)

The base 10 notation is then generated as follows.

(x^y means x to the yth power)

0101 -> 0 x 2^3 + 1 x 2^2 + 0 x 2^1 + 1 x 2^0 = 5,

or

0101 -> 0 x 8 + 1 x 4 + 0 x 2 + 1 x 1 = 5,

or

0101 -> 5

0101 (base 2) converted to base 10 is therefore: 5

2)

The base 10 notation is then generated as follows.

(x^y means x to the yth power)

1001 -> 1 x 2^3 + 0 x 2^2 + 0 x 2^1 + 1 x 2^0 = 9,

or

1001 -> 1 x 8 + 0 x 4 + 0 x 2 + 1 x 1 = 9,

or

1001 -> 9

1001 (base 2) converted to base 10 is therefore: 9

3)

The base 10 notation is then generated as follows.

(x^y means x to the yth power)

1+011 -> 1 x 2^4 + + x 2^3 + 0 x 2^2 + 1 x 2^1 + 1 x 2^0 = 19,

or

1+011 -> 1 x 16 + + x 8 + 0 x 4 + 1 x 2 + 1 x 1 = 19,

or

1+011 -> 19

1+011 (base 2) converted to base 10 is therefore: 19

4)

The base 10 notation is then generated as follows.

(x^y means x to the yth power)

0110 -> 0 x 2^3 + 1 x 2^2 + 1 x 2^1 + 0 x 2^0 = 6,

or

0110 -> 0 x 8 + 1 x 4 + 1 x 2 + 0 x 1 = 6,

or

0110 -> 6

0110 (base 2) converted to base 10 is therefore: 6

5)

The base 10 notation is then generated as follows.

(x^y means x to the yth power)

10000 -> 1 x 2^4 + 0 x 2^3 + 0 x 2^2 + 0 x 2^1 + 0 x 2^0 = 16,

or

10000 -> 1 x 16 + 0 x 8 + 0 x 4 + 0 x 2 + 0 x 1 = 16,

or

10000 -> 16

10000 (base 2) converted to base 10 is therefore: 16

Explanation: