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;
- 19 230 767 ÷ 2 = 9 615 383 + 1;
- 9 615 383 ÷ 2 = 4 807 691 + 1;
- 4 807 691 ÷ 2 = 2 403 845 + 1;
- 2 403 845 ÷ 2 = 1 201 922 + 1;
- 1 201 922 ÷ 2 = 600 961 + 0;
- 600 961 ÷ 2 = 300 480 + 1;
- 300 480 ÷ 2 = 150 240 + 0;
- 150 240 ÷ 2 = 75 120 + 0;
- 75 120 ÷ 2 = 37 560 + 0;
- 37 560 ÷ 2 = 18 780 + 0;
- 18 780 ÷ 2 = 9 390 + 0;
- 9 390 ÷ 2 = 4 695 + 0;
- 4 695 ÷ 2 = 2 347 + 1;
- 2 347 ÷ 2 = 1 173 + 1;
- 1 173 ÷ 2 = 586 + 1;
- 586 ÷ 2 = 293 + 0;
- 293 ÷ 2 = 146 + 1;
- 146 ÷ 2 = 73 + 0;
- 73 ÷ 2 = 36 + 1;
- 36 ÷ 2 = 18 + 0;
- 18 ÷ 2 = 9 + 0;
- 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.
19 230 767(10) = 1 0010 0101 0111 0000 0010 1111(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 25.
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, 25,
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 19 230 767(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
19 230 767(10) = 0000 0001 0010 0101 0111 0000 0010 1111
Spaces were used to group digits: for binary, by 4, for decimal, by 3.