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;
- 1 100 110 111 011 147 ÷ 2 = 550 055 055 505 573 + 1;
- 550 055 055 505 573 ÷ 2 = 275 027 527 752 786 + 1;
- 275 027 527 752 786 ÷ 2 = 137 513 763 876 393 + 0;
- 137 513 763 876 393 ÷ 2 = 68 756 881 938 196 + 1;
- 68 756 881 938 196 ÷ 2 = 34 378 440 969 098 + 0;
- 34 378 440 969 098 ÷ 2 = 17 189 220 484 549 + 0;
- 17 189 220 484 549 ÷ 2 = 8 594 610 242 274 + 1;
- 8 594 610 242 274 ÷ 2 = 4 297 305 121 137 + 0;
- 4 297 305 121 137 ÷ 2 = 2 148 652 560 568 + 1;
- 2 148 652 560 568 ÷ 2 = 1 074 326 280 284 + 0;
- 1 074 326 280 284 ÷ 2 = 537 163 140 142 + 0;
- 537 163 140 142 ÷ 2 = 268 581 570 071 + 0;
- 268 581 570 071 ÷ 2 = 134 290 785 035 + 1;
- 134 290 785 035 ÷ 2 = 67 145 392 517 + 1;
- 67 145 392 517 ÷ 2 = 33 572 696 258 + 1;
- 33 572 696 258 ÷ 2 = 16 786 348 129 + 0;
- 16 786 348 129 ÷ 2 = 8 393 174 064 + 1;
- 8 393 174 064 ÷ 2 = 4 196 587 032 + 0;
- 4 196 587 032 ÷ 2 = 2 098 293 516 + 0;
- 2 098 293 516 ÷ 2 = 1 049 146 758 + 0;
- 1 049 146 758 ÷ 2 = 524 573 379 + 0;
- 524 573 379 ÷ 2 = 262 286 689 + 1;
- 262 286 689 ÷ 2 = 131 143 344 + 1;
- 131 143 344 ÷ 2 = 65 571 672 + 0;
- 65 571 672 ÷ 2 = 32 785 836 + 0;
- 32 785 836 ÷ 2 = 16 392 918 + 0;
- 16 392 918 ÷ 2 = 8 196 459 + 0;
- 8 196 459 ÷ 2 = 4 098 229 + 1;
- 4 098 229 ÷ 2 = 2 049 114 + 1;
- 2 049 114 ÷ 2 = 1 024 557 + 0;
- 1 024 557 ÷ 2 = 512 278 + 1;
- 512 278 ÷ 2 = 256 139 + 0;
- 256 139 ÷ 2 = 128 069 + 1;
- 128 069 ÷ 2 = 64 034 + 1;
- 64 034 ÷ 2 = 32 017 + 0;
- 32 017 ÷ 2 = 16 008 + 1;
- 16 008 ÷ 2 = 8 004 + 0;
- 8 004 ÷ 2 = 4 002 + 0;
- 4 002 ÷ 2 = 2 001 + 0;
- 2 001 ÷ 2 = 1 000 + 1;
- 1 000 ÷ 2 = 500 + 0;
- 500 ÷ 2 = 250 + 0;
- 250 ÷ 2 = 125 + 0;
- 125 ÷ 2 = 62 + 1;
- 62 ÷ 2 = 31 + 0;
- 31 ÷ 2 = 15 + 1;
- 15 ÷ 2 = 7 + 1;
- 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.
1 100 110 111 011 147(10) = 11 1110 1000 1000 1011 0101 1000 0110 0001 0111 0001 0100 1011(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 50.
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, 50,
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 1 100 110 111 011 147(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:
1 100 110 111 011 147(10) = 0000 0000 0000 0011 1110 1000 1000 1011 0101 1000 0110 0001 0111 0001 0100 1011
Spaces were used to group digits: for binary, by 4, for decimal, by 3.