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;
- 736 662 003 ÷ 2 = 368 331 001 + 1;
- 368 331 001 ÷ 2 = 184 165 500 + 1;
- 184 165 500 ÷ 2 = 92 082 750 + 0;
- 92 082 750 ÷ 2 = 46 041 375 + 0;
- 46 041 375 ÷ 2 = 23 020 687 + 1;
- 23 020 687 ÷ 2 = 11 510 343 + 1;
- 11 510 343 ÷ 2 = 5 755 171 + 1;
- 5 755 171 ÷ 2 = 2 877 585 + 1;
- 2 877 585 ÷ 2 = 1 438 792 + 1;
- 1 438 792 ÷ 2 = 719 396 + 0;
- 719 396 ÷ 2 = 359 698 + 0;
- 359 698 ÷ 2 = 179 849 + 0;
- 179 849 ÷ 2 = 89 924 + 1;
- 89 924 ÷ 2 = 44 962 + 0;
- 44 962 ÷ 2 = 22 481 + 0;
- 22 481 ÷ 2 = 11 240 + 1;
- 11 240 ÷ 2 = 5 620 + 0;
- 5 620 ÷ 2 = 2 810 + 0;
- 2 810 ÷ 2 = 1 405 + 0;
- 1 405 ÷ 2 = 702 + 1;
- 702 ÷ 2 = 351 + 0;
- 351 ÷ 2 = 175 + 1;
- 175 ÷ 2 = 87 + 1;
- 87 ÷ 2 = 43 + 1;
- 43 ÷ 2 = 21 + 1;
- 21 ÷ 2 = 10 + 1;
- 10 ÷ 2 = 5 + 0;
- 5 ÷ 2 = 2 + 1;
- 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.
736 662 003(10) = 10 1011 1110 1000 1001 0001 1111 0011(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 30.
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, 30,
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 736 662 003(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
736 662 003(10) = 0010 1011 1110 1000 1001 0001 1111 0011
Spaces were used to group digits: for binary, by 4, for decimal, by 3.