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;
- 1 011 001 100 947 ÷ 2 = 505 500 550 473 + 1;
- 505 500 550 473 ÷ 2 = 252 750 275 236 + 1;
- 252 750 275 236 ÷ 2 = 126 375 137 618 + 0;
- 126 375 137 618 ÷ 2 = 63 187 568 809 + 0;
- 63 187 568 809 ÷ 2 = 31 593 784 404 + 1;
- 31 593 784 404 ÷ 2 = 15 796 892 202 + 0;
- 15 796 892 202 ÷ 2 = 7 898 446 101 + 0;
- 7 898 446 101 ÷ 2 = 3 949 223 050 + 1;
- 3 949 223 050 ÷ 2 = 1 974 611 525 + 0;
- 1 974 611 525 ÷ 2 = 987 305 762 + 1;
- 987 305 762 ÷ 2 = 493 652 881 + 0;
- 493 652 881 ÷ 2 = 246 826 440 + 1;
- 246 826 440 ÷ 2 = 123 413 220 + 0;
- 123 413 220 ÷ 2 = 61 706 610 + 0;
- 61 706 610 ÷ 2 = 30 853 305 + 0;
- 30 853 305 ÷ 2 = 15 426 652 + 1;
- 15 426 652 ÷ 2 = 7 713 326 + 0;
- 7 713 326 ÷ 2 = 3 856 663 + 0;
- 3 856 663 ÷ 2 = 1 928 331 + 1;
- 1 928 331 ÷ 2 = 964 165 + 1;
- 964 165 ÷ 2 = 482 082 + 1;
- 482 082 ÷ 2 = 241 041 + 0;
- 241 041 ÷ 2 = 120 520 + 1;
- 120 520 ÷ 2 = 60 260 + 0;
- 60 260 ÷ 2 = 30 130 + 0;
- 30 130 ÷ 2 = 15 065 + 0;
- 15 065 ÷ 2 = 7 532 + 1;
- 7 532 ÷ 2 = 3 766 + 0;
- 3 766 ÷ 2 = 1 883 + 0;
- 1 883 ÷ 2 = 941 + 1;
- 941 ÷ 2 = 470 + 1;
- 470 ÷ 2 = 235 + 0;
- 235 ÷ 2 = 117 + 1;
- 117 ÷ 2 = 58 + 1;
- 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.
1 011 001 100 947(10) = 1110 1011 0110 0100 0101 1100 1000 1010 1001 0011(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 1 011 001 100 947(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:
Spaces were used to group digits: for binary, by 4, for decimal, by 3.