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;
- 101 001 101 175 ÷ 2 = 50 500 550 587 + 1;
- 50 500 550 587 ÷ 2 = 25 250 275 293 + 1;
- 25 250 275 293 ÷ 2 = 12 625 137 646 + 1;
- 12 625 137 646 ÷ 2 = 6 312 568 823 + 0;
- 6 312 568 823 ÷ 2 = 3 156 284 411 + 1;
- 3 156 284 411 ÷ 2 = 1 578 142 205 + 1;
- 1 578 142 205 ÷ 2 = 789 071 102 + 1;
- 789 071 102 ÷ 2 = 394 535 551 + 0;
- 394 535 551 ÷ 2 = 197 267 775 + 1;
- 197 267 775 ÷ 2 = 98 633 887 + 1;
- 98 633 887 ÷ 2 = 49 316 943 + 1;
- 49 316 943 ÷ 2 = 24 658 471 + 1;
- 24 658 471 ÷ 2 = 12 329 235 + 1;
- 12 329 235 ÷ 2 = 6 164 617 + 1;
- 6 164 617 ÷ 2 = 3 082 308 + 1;
- 3 082 308 ÷ 2 = 1 541 154 + 0;
- 1 541 154 ÷ 2 = 770 577 + 0;
- 770 577 ÷ 2 = 385 288 + 1;
- 385 288 ÷ 2 = 192 644 + 0;
- 192 644 ÷ 2 = 96 322 + 0;
- 96 322 ÷ 2 = 48 161 + 0;
- 48 161 ÷ 2 = 24 080 + 1;
- 24 080 ÷ 2 = 12 040 + 0;
- 12 040 ÷ 2 = 6 020 + 0;
- 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.
101 001 101 175(10) = 1 0111 1000 0100 0010 0010 0111 1111 0111 0111(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) 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, 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 101 001 101 175(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:
101 001 101 175(10) = 0000 0000 0000 0000 0000 0000 0001 0111 1000 0100 0010 0010 0111 1111 0111 0111
Spaces were used to group digits: for binary, by 4, for decimal, by 3.