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;
- 1 100 001 110 067 ÷ 2 = 550 000 555 033 + 1;
- 550 000 555 033 ÷ 2 = 275 000 277 516 + 1;
- 275 000 277 516 ÷ 2 = 137 500 138 758 + 0;
- 137 500 138 758 ÷ 2 = 68 750 069 379 + 0;
- 68 750 069 379 ÷ 2 = 34 375 034 689 + 1;
- 34 375 034 689 ÷ 2 = 17 187 517 344 + 1;
- 17 187 517 344 ÷ 2 = 8 593 758 672 + 0;
- 8 593 758 672 ÷ 2 = 4 296 879 336 + 0;
- 4 296 879 336 ÷ 2 = 2 148 439 668 + 0;
- 2 148 439 668 ÷ 2 = 1 074 219 834 + 0;
- 1 074 219 834 ÷ 2 = 537 109 917 + 0;
- 537 109 917 ÷ 2 = 268 554 958 + 1;
- 268 554 958 ÷ 2 = 134 277 479 + 0;
- 134 277 479 ÷ 2 = 67 138 739 + 1;
- 67 138 739 ÷ 2 = 33 569 369 + 1;
- 33 569 369 ÷ 2 = 16 784 684 + 1;
- 16 784 684 ÷ 2 = 8 392 342 + 0;
- 8 392 342 ÷ 2 = 4 196 171 + 0;
- 4 196 171 ÷ 2 = 2 098 085 + 1;
- 2 098 085 ÷ 2 = 1 049 042 + 1;
- 1 049 042 ÷ 2 = 524 521 + 0;
- 524 521 ÷ 2 = 262 260 + 1;
- 262 260 ÷ 2 = 131 130 + 0;
- 131 130 ÷ 2 = 65 565 + 0;
- 65 565 ÷ 2 = 32 782 + 1;
- 32 782 ÷ 2 = 16 391 + 0;
- 16 391 ÷ 2 = 8 195 + 1;
- 8 195 ÷ 2 = 4 097 + 1;
- 4 097 ÷ 2 = 2 048 + 1;
- 2 048 ÷ 2 = 1 024 + 0;
- 1 024 ÷ 2 = 512 + 0;
- 512 ÷ 2 = 256 + 0;
- 256 ÷ 2 = 128 + 0;
- 128 ÷ 2 = 64 + 0;
- 64 ÷ 2 = 32 + 0;
- 32 ÷ 2 = 16 + 0;
- 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.
1 100 001 110 067(10) = 1 0000 0000 0001 1101 0010 1100 1110 1000 0011 0011(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 41.
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, 41,
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 1 100 001 110 067(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:
1 100 001 110 067(10) = 0000 0000 0000 0000 0000 0001 0000 0000 0001 1101 0010 1100 1110 1000 0011 0011
Spaces were used to group digits: for binary, by 4, for decimal, by 3.