Convert base two (2) number 1 1110 1101 1111 to base ten (10): the unsigned binary number converted to a positive integer written in the decimal system

Unsigned binary (base 2) 1 1110 1101 1111_{(2)} to a positive integer (no sign) in decimal system (in base 10) = ?

1. Map the unsigned binary number's digits versus the corresponding powers of 2 that their place value represent:

2^{12}

1

2^{11}

1

2^{10}

1

2^{9}

1

2^{8}

0

2^{7}

1

2^{6}

1

2^{5}

0

2^{4}

1

2^{3}

1

2^{2}

1

2^{1}

1

2^{0}

1

2. Multiply each bit by its corresponding power of 2 and add all the terms up:

Number 1 1110 1101 1111_{(2)} converted from unsigned binary (base 2) to positive integer (no sign) in decimal system (in base 10): 1 1110 1101 1111_{(2)} = 7 903_{(10)}

Spaces used to group digits: for binary, by 4; for decimal, by 3.

How to convert unsigned binary numbers from binary system to decimal? Simply convert from base two to base ten.

To understand how to convert a number from base two to base ten, the easiest way is to do it through an example - convert the number from base two, 101 0011_{(2)}, to base ten:

Write bellow the binary number in base two, and above each bit that makes up the binary number write the corresponding power of 2 (numeral base) that its place value represents, starting with zero, from the right of the number (rightmost bit), walking to the left of the number, increasing each corresponding power of 2 by exactly one unit each time we move to the left:

powers of 2:

6

5

4

3

2

1

0

digits:

1

0

1

0

0

1

1

Build the representation of the positive number in base 10, by taking each digit of the binary number, multiplying it by the corresponding power of 2 and then adding all the terms up: