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;
- 111 101 010 989 ÷ 2 = 55 550 505 494 + 1;
- 55 550 505 494 ÷ 2 = 27 775 252 747 + 0;
- 27 775 252 747 ÷ 2 = 13 887 626 373 + 1;
- 13 887 626 373 ÷ 2 = 6 943 813 186 + 1;
- 6 943 813 186 ÷ 2 = 3 471 906 593 + 0;
- 3 471 906 593 ÷ 2 = 1 735 953 296 + 1;
- 1 735 953 296 ÷ 2 = 867 976 648 + 0;
- 867 976 648 ÷ 2 = 433 988 324 + 0;
- 433 988 324 ÷ 2 = 216 994 162 + 0;
- 216 994 162 ÷ 2 = 108 497 081 + 0;
- 108 497 081 ÷ 2 = 54 248 540 + 1;
- 54 248 540 ÷ 2 = 27 124 270 + 0;
- 27 124 270 ÷ 2 = 13 562 135 + 0;
- 13 562 135 ÷ 2 = 6 781 067 + 1;
- 6 781 067 ÷ 2 = 3 390 533 + 1;
- 3 390 533 ÷ 2 = 1 695 266 + 1;
- 1 695 266 ÷ 2 = 847 633 + 0;
- 847 633 ÷ 2 = 423 816 + 1;
- 423 816 ÷ 2 = 211 908 + 0;
- 211 908 ÷ 2 = 105 954 + 0;
- 105 954 ÷ 2 = 52 977 + 0;
- 52 977 ÷ 2 = 26 488 + 1;
- 26 488 ÷ 2 = 13 244 + 0;
- 13 244 ÷ 2 = 6 622 + 0;
- 6 622 ÷ 2 = 3 311 + 0;
- 3 311 ÷ 2 = 1 655 + 1;
- 1 655 ÷ 2 = 827 + 1;
- 827 ÷ 2 = 413 + 1;
- 413 ÷ 2 = 206 + 1;
- 206 ÷ 2 = 103 + 0;
- 103 ÷ 2 = 51 + 1;
- 51 ÷ 2 = 25 + 1;
- 25 ÷ 2 = 12 + 1;
- 12 ÷ 2 = 6 + 0;
- 6 ÷ 2 = 3 + 0;
- 3 ÷ 2 = 1 + 1;
- 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.
111 101 010 989(10) = 1 1001 1101 1110 0010 0010 1110 0100 0010 1101(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 37.
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) indicates 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, 37,
3) so that the first bit (leftmost) could be zero
(we deal with a positive number at this moment)
=== is: 64.
4. Get the positive binary computer representation on 64 bits (8 Bytes):
If needed, add extra 0s in front (to the left) of the base 2 number, up to the required length, 64.
Number 111 101 010 989(10), a signed integer number (with sign), converted from decimal system (from base 10) and written as a signed binary in one's complement representation:
111 101 010 989(10) = 0000 0000 0000 0000 0000 0000 0001 1001 1101 1110 0010 0010 1110 0100 0010 1101
Spaces were used to group digits: for binary, by 4, for decimal, by 3.