1. Divide the number repeatedly by 2:
Keep track of each remainder.
We stop when we get a quotient that is equal to zero.
- division = quotient + remainder;
- 4 999 987 ÷ 2 = 2 499 993 + 1;
- 2 499 993 ÷ 2 = 1 249 996 + 1;
- 1 249 996 ÷ 2 = 624 998 + 0;
- 624 998 ÷ 2 = 312 499 + 0;
- 312 499 ÷ 2 = 156 249 + 1;
- 156 249 ÷ 2 = 78 124 + 1;
- 78 124 ÷ 2 = 39 062 + 0;
- 39 062 ÷ 2 = 19 531 + 0;
- 19 531 ÷ 2 = 9 765 + 1;
- 9 765 ÷ 2 = 4 882 + 1;
- 4 882 ÷ 2 = 2 441 + 0;
- 2 441 ÷ 2 = 1 220 + 1;
- 1 220 ÷ 2 = 610 + 0;
- 610 ÷ 2 = 305 + 0;
- 305 ÷ 2 = 152 + 1;
- 152 ÷ 2 = 76 + 0;
- 76 ÷ 2 = 38 + 0;
- 38 ÷ 2 = 19 + 0;
- 19 ÷ 2 = 9 + 1;
- 9 ÷ 2 = 4 + 1;
- 4 ÷ 2 = 2 + 0;
- 2 ÷ 2 = 1 + 0;
- 1 ÷ 2 = 0 + 1;
2. Construct the base 2 representation of the positive number:
Take all the remainders starting from the bottom of the list constructed above.
4 999 987(10) = 100 1100 0100 1011 0011 0011(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 23.
A signed binary's bit length must be equal to a power of 2, as of:
21 = 2; 22 = 4; 23 = 8; 24 = 16; 25 = 32; 26 = 64; ...
The first bit (the leftmost) is reserved for the sign:
0 = positive integer number, 1 = negative integer number
The least number that is:
1) a power of 2
2) and is larger than the actual length, 23,
3) so that the first bit (leftmost) could be zero
(we deal with a positive number at this moment)
=== is: 32.
4. Get the positive binary computer representation on 32 bits (4 Bytes):
If needed, add extra 0s in front (to the left) of the base 2 number, up to the required length, 32:
Number 4 999 987(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
4 999 987(10) = 0000 0000 0100 1100 0100 1011 0011 0011
Spaces were used to group digits: for binary, by 4, for decimal, by 3.