NASARAWAPOLY: how do I convert 7.875 to binary?

richronet

8 years ago

1. We start with the positive version of the number:

-7.875| = 7.875

2. First, convert to binary (base 2) the integer part: 7. Divide the number repeatedly by 2, keeping track of each remainder, until we get a quotient that is equal to zero:

division = quotient + remainder;
7 ÷ 2 = 3 + 1;
3 ÷ 2 = 1 + 1;
1 ÷ 2 = 0 + 1;
3. Construct the base 2 representation of the integer part of the number, by taking all the remainders starting from the bottom of the list constructed above:

7(10) =

111(2)

4. Convert to binary (base 2) the fractional part: 0.875. Multiply it repeatedly by 2, keeping track of each integer part of the results, until we get a fractional part that is equal to zero:

#) multiplying = integer + fractional part;
1) 0.875 × 2 = 1 + 0.75;
2) 0.75 × 2 = 1 + 0.5;
3) 0.5 × 2 = 1 + 0;
5. Construct the base 2 representation of the fractional part of the number, by taking all the integer parts of the multiplying operations, starting from the top of the constructed list above:

0.875(10) =

0.111(2)

Positive number before normalization:

7.875(10) =

111.111(base2)