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;
- 148 424 101 472 920 ÷ 2 = 74 212 050 736 460 + 0;
- 74 212 050 736 460 ÷ 2 = 37 106 025 368 230 + 0;
- 37 106 025 368 230 ÷ 2 = 18 553 012 684 115 + 0;
- 18 553 012 684 115 ÷ 2 = 9 276 506 342 057 + 1;
- 9 276 506 342 057 ÷ 2 = 4 638 253 171 028 + 1;
- 4 638 253 171 028 ÷ 2 = 2 319 126 585 514 + 0;
- 2 319 126 585 514 ÷ 2 = 1 159 563 292 757 + 0;
- 1 159 563 292 757 ÷ 2 = 579 781 646 378 + 1;
- 579 781 646 378 ÷ 2 = 289 890 823 189 + 0;
- 289 890 823 189 ÷ 2 = 144 945 411 594 + 1;
- 144 945 411 594 ÷ 2 = 72 472 705 797 + 0;
- 72 472 705 797 ÷ 2 = 36 236 352 898 + 1;
- 36 236 352 898 ÷ 2 = 18 118 176 449 + 0;
- 18 118 176 449 ÷ 2 = 9 059 088 224 + 1;
- 9 059 088 224 ÷ 2 = 4 529 544 112 + 0;
- 4 529 544 112 ÷ 2 = 2 264 772 056 + 0;
- 2 264 772 056 ÷ 2 = 1 132 386 028 + 0;
- 1 132 386 028 ÷ 2 = 566 193 014 + 0;
- 566 193 014 ÷ 2 = 283 096 507 + 0;
- 283 096 507 ÷ 2 = 141 548 253 + 1;
- 141 548 253 ÷ 2 = 70 774 126 + 1;
- 70 774 126 ÷ 2 = 35 387 063 + 0;
- 35 387 063 ÷ 2 = 17 693 531 + 1;
- 17 693 531 ÷ 2 = 8 846 765 + 1;
- 8 846 765 ÷ 2 = 4 423 382 + 1;
- 4 423 382 ÷ 2 = 2 211 691 + 0;
- 2 211 691 ÷ 2 = 1 105 845 + 1;
- 1 105 845 ÷ 2 = 552 922 + 1;
- 552 922 ÷ 2 = 276 461 + 0;
- 276 461 ÷ 2 = 138 230 + 1;
- 138 230 ÷ 2 = 69 115 + 0;
- 69 115 ÷ 2 = 34 557 + 1;
- 34 557 ÷ 2 = 17 278 + 1;
- 17 278 ÷ 2 = 8 639 + 0;
- 8 639 ÷ 2 = 4 319 + 1;
- 4 319 ÷ 2 = 2 159 + 1;
- 2 159 ÷ 2 = 1 079 + 1;
- 1 079 ÷ 2 = 539 + 1;
- 539 ÷ 2 = 269 + 1;
- 269 ÷ 2 = 134 + 1;
- 134 ÷ 2 = 67 + 0;
- 67 ÷ 2 = 33 + 1;
- 33 ÷ 2 = 16 + 1;
- 16 ÷ 2 = 8 + 0;
- 8 ÷ 2 = 4 + 0;
- 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.
148 424 101 472 920(10) = 1000 0110 1111 1101 1010 1101 1101 1000 0010 1010 1001 1000(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 48.
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, 48,
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 148 424 101 472 920(10), a signed integer number (with sign), converted from decimal system (from base 10) and written as a signed binary in two's complement representation:
148 424 101 472 920(10) = 0000 0000 0000 0000 1000 0110 1111 1101 1010 1101 1101 1000 0010 1010 1001 1000
Spaces were used to group digits: for binary, by 4, for decimal, by 3.