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;
- 101 011 001 012 ÷ 2 = 50 505 500 506 + 0;
- 50 505 500 506 ÷ 2 = 25 252 750 253 + 0;
- 25 252 750 253 ÷ 2 = 12 626 375 126 + 1;
- 12 626 375 126 ÷ 2 = 6 313 187 563 + 0;
- 6 313 187 563 ÷ 2 = 3 156 593 781 + 1;
- 3 156 593 781 ÷ 2 = 1 578 296 890 + 1;
- 1 578 296 890 ÷ 2 = 789 148 445 + 0;
- 789 148 445 ÷ 2 = 394 574 222 + 1;
- 394 574 222 ÷ 2 = 197 287 111 + 0;
- 197 287 111 ÷ 2 = 98 643 555 + 1;
- 98 643 555 ÷ 2 = 49 321 777 + 1;
- 49 321 777 ÷ 2 = 24 660 888 + 1;
- 24 660 888 ÷ 2 = 12 330 444 + 0;
- 12 330 444 ÷ 2 = 6 165 222 + 0;
- 6 165 222 ÷ 2 = 3 082 611 + 0;
- 3 082 611 ÷ 2 = 1 541 305 + 1;
- 1 541 305 ÷ 2 = 770 652 + 1;
- 770 652 ÷ 2 = 385 326 + 0;
- 385 326 ÷ 2 = 192 663 + 0;
- 192 663 ÷ 2 = 96 331 + 1;
- 96 331 ÷ 2 = 48 165 + 1;
- 48 165 ÷ 2 = 24 082 + 1;
- 24 082 ÷ 2 = 12 041 + 0;
- 12 041 ÷ 2 = 6 020 + 1;
- 6 020 ÷ 2 = 3 010 + 0;
- 3 010 ÷ 2 = 1 505 + 0;
- 1 505 ÷ 2 = 752 + 1;
- 752 ÷ 2 = 376 + 0;
- 376 ÷ 2 = 188 + 0;
- 188 ÷ 2 = 94 + 0;
- 94 ÷ 2 = 47 + 0;
- 47 ÷ 2 = 23 + 1;
- 23 ÷ 2 = 11 + 1;
- 11 ÷ 2 = 5 + 1;
- 5 ÷ 2 = 2 + 1;
- 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.
101 011 001 012(10) = 1 0111 1000 0100 1011 1001 1000 1110 1011 0100(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 37.
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) is reserved for 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, 37,
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 101 011 001 012(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
101 011 001 012(10) = 0000 0000 0000 0000 0000 0000 0001 0111 1000 0100 1011 1001 1000 1110 1011 0100
Spaces were used to group digits: for binary, by 4, for decimal, by 3.