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;
- 1 100 101 110 010 184 ÷ 2 = 550 050 555 005 092 + 0;
- 550 050 555 005 092 ÷ 2 = 275 025 277 502 546 + 0;
- 275 025 277 502 546 ÷ 2 = 137 512 638 751 273 + 0;
- 137 512 638 751 273 ÷ 2 = 68 756 319 375 636 + 1;
- 68 756 319 375 636 ÷ 2 = 34 378 159 687 818 + 0;
- 34 378 159 687 818 ÷ 2 = 17 189 079 843 909 + 0;
- 17 189 079 843 909 ÷ 2 = 8 594 539 921 954 + 1;
- 8 594 539 921 954 ÷ 2 = 4 297 269 960 977 + 0;
- 4 297 269 960 977 ÷ 2 = 2 148 634 980 488 + 1;
- 2 148 634 980 488 ÷ 2 = 1 074 317 490 244 + 0;
- 1 074 317 490 244 ÷ 2 = 537 158 745 122 + 0;
- 537 158 745 122 ÷ 2 = 268 579 372 561 + 0;
- 268 579 372 561 ÷ 2 = 134 289 686 280 + 1;
- 134 289 686 280 ÷ 2 = 67 144 843 140 + 0;
- 67 144 843 140 ÷ 2 = 33 572 421 570 + 0;
- 33 572 421 570 ÷ 2 = 16 786 210 785 + 0;
- 16 786 210 785 ÷ 2 = 8 393 105 392 + 1;
- 8 393 105 392 ÷ 2 = 4 196 552 696 + 0;
- 4 196 552 696 ÷ 2 = 2 098 276 348 + 0;
- 2 098 276 348 ÷ 2 = 1 049 138 174 + 0;
- 1 049 138 174 ÷ 2 = 524 569 087 + 0;
- 524 569 087 ÷ 2 = 262 284 543 + 1;
- 262 284 543 ÷ 2 = 131 142 271 + 1;
- 131 142 271 ÷ 2 = 65 571 135 + 1;
- 65 571 135 ÷ 2 = 32 785 567 + 1;
- 32 785 567 ÷ 2 = 16 392 783 + 1;
- 16 392 783 ÷ 2 = 8 196 391 + 1;
- 8 196 391 ÷ 2 = 4 098 195 + 1;
- 4 098 195 ÷ 2 = 2 049 097 + 1;
- 2 049 097 ÷ 2 = 1 024 548 + 1;
- 1 024 548 ÷ 2 = 512 274 + 0;
- 512 274 ÷ 2 = 256 137 + 0;
- 256 137 ÷ 2 = 128 068 + 1;
- 128 068 ÷ 2 = 64 034 + 0;
- 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.
1 100 101 110 010 184(10) = 11 1110 1000 1000 1001 0011 1111 1110 0001 0001 0001 0100 1000(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 1 100 101 110 010 184(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:
1 100 101 110 010 184(10) = 0000 0000 0000 0011 1110 1000 1000 1001 0011 1111 1110 0001 0001 0001 0100 1000
Spaces were used to group digits: for binary, by 4, for decimal, by 3.