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;
- 1 227 133 497 ÷ 2 = 613 566 748 + 1;
- 613 566 748 ÷ 2 = 306 783 374 + 0;
- 306 783 374 ÷ 2 = 153 391 687 + 0;
- 153 391 687 ÷ 2 = 76 695 843 + 1;
- 76 695 843 ÷ 2 = 38 347 921 + 1;
- 38 347 921 ÷ 2 = 19 173 960 + 1;
- 19 173 960 ÷ 2 = 9 586 980 + 0;
- 9 586 980 ÷ 2 = 4 793 490 + 0;
- 4 793 490 ÷ 2 = 2 396 745 + 0;
- 2 396 745 ÷ 2 = 1 198 372 + 1;
- 1 198 372 ÷ 2 = 599 186 + 0;
- 599 186 ÷ 2 = 299 593 + 0;
- 299 593 ÷ 2 = 149 796 + 1;
- 149 796 ÷ 2 = 74 898 + 0;
- 74 898 ÷ 2 = 37 449 + 0;
- 37 449 ÷ 2 = 18 724 + 1;
- 18 724 ÷ 2 = 9 362 + 0;
- 9 362 ÷ 2 = 4 681 + 0;
- 4 681 ÷ 2 = 2 340 + 1;
- 2 340 ÷ 2 = 1 170 + 0;
- 1 170 ÷ 2 = 585 + 0;
- 585 ÷ 2 = 292 + 1;
- 292 ÷ 2 = 146 + 0;
- 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.
1 227 133 497(10) = 100 1001 0010 0100 1001 0010 0011 1001(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 31.
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, 31,
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 1 227 133 497(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
1 227 133 497(10) = 0100 1001 0010 0100 1001 0010 0011 1001
Spaces were used to group digits: for binary, by 4, for decimal, by 3.