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;
- 1 001 110 100 040 ÷ 2 = 500 555 050 020 + 0;
- 500 555 050 020 ÷ 2 = 250 277 525 010 + 0;
- 250 277 525 010 ÷ 2 = 125 138 762 505 + 0;
- 125 138 762 505 ÷ 2 = 62 569 381 252 + 1;
- 62 569 381 252 ÷ 2 = 31 284 690 626 + 0;
- 31 284 690 626 ÷ 2 = 15 642 345 313 + 0;
- 15 642 345 313 ÷ 2 = 7 821 172 656 + 1;
- 7 821 172 656 ÷ 2 = 3 910 586 328 + 0;
- 3 910 586 328 ÷ 2 = 1 955 293 164 + 0;
- 1 955 293 164 ÷ 2 = 977 646 582 + 0;
- 977 646 582 ÷ 2 = 488 823 291 + 0;
- 488 823 291 ÷ 2 = 244 411 645 + 1;
- 244 411 645 ÷ 2 = 122 205 822 + 1;
- 122 205 822 ÷ 2 = 61 102 911 + 0;
- 61 102 911 ÷ 2 = 30 551 455 + 1;
- 30 551 455 ÷ 2 = 15 275 727 + 1;
- 15 275 727 ÷ 2 = 7 637 863 + 1;
- 7 637 863 ÷ 2 = 3 818 931 + 1;
- 3 818 931 ÷ 2 = 1 909 465 + 1;
- 1 909 465 ÷ 2 = 954 732 + 1;
- 954 732 ÷ 2 = 477 366 + 0;
- 477 366 ÷ 2 = 238 683 + 0;
- 238 683 ÷ 2 = 119 341 + 1;
- 119 341 ÷ 2 = 59 670 + 1;
- 59 670 ÷ 2 = 29 835 + 0;
- 29 835 ÷ 2 = 14 917 + 1;
- 14 917 ÷ 2 = 7 458 + 1;
- 7 458 ÷ 2 = 3 729 + 0;
- 3 729 ÷ 2 = 1 864 + 1;
- 1 864 ÷ 2 = 932 + 0;
- 932 ÷ 2 = 466 + 0;
- 466 ÷ 2 = 233 + 0;
- 233 ÷ 2 = 116 + 1;
- 116 ÷ 2 = 58 + 0;
- 58 ÷ 2 = 29 + 0;
- 29 ÷ 2 = 14 + 1;
- 14 ÷ 2 = 7 + 0;
- 7 ÷ 2 = 3 + 1;
- 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.
1 001 110 100 040(10) = 1110 1001 0001 0110 1100 1111 1101 1000 0100 1000(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 40.
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, 40,
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 1 001 110 100 040(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:
1 001 110 100 040(10) = 0000 0000 0000 0000 0000 0000 1110 1001 0001 0110 1100 1111 1101 1000 0100 1000
Spaces were used to group digits: for binary, by 4, for decimal, by 3.