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;
- 17 227 214 209 ÷ 2 = 8 613 607 104 + 1;
- 8 613 607 104 ÷ 2 = 4 306 803 552 + 0;
- 4 306 803 552 ÷ 2 = 2 153 401 776 + 0;
- 2 153 401 776 ÷ 2 = 1 076 700 888 + 0;
- 1 076 700 888 ÷ 2 = 538 350 444 + 0;
- 538 350 444 ÷ 2 = 269 175 222 + 0;
- 269 175 222 ÷ 2 = 134 587 611 + 0;
- 134 587 611 ÷ 2 = 67 293 805 + 1;
- 67 293 805 ÷ 2 = 33 646 902 + 1;
- 33 646 902 ÷ 2 = 16 823 451 + 0;
- 16 823 451 ÷ 2 = 8 411 725 + 1;
- 8 411 725 ÷ 2 = 4 205 862 + 1;
- 4 205 862 ÷ 2 = 2 102 931 + 0;
- 2 102 931 ÷ 2 = 1 051 465 + 1;
- 1 051 465 ÷ 2 = 525 732 + 1;
- 525 732 ÷ 2 = 262 866 + 0;
- 262 866 ÷ 2 = 131 433 + 0;
- 131 433 ÷ 2 = 65 716 + 1;
- 65 716 ÷ 2 = 32 858 + 0;
- 32 858 ÷ 2 = 16 429 + 0;
- 16 429 ÷ 2 = 8 214 + 1;
- 8 214 ÷ 2 = 4 107 + 0;
- 4 107 ÷ 2 = 2 053 + 1;
- 2 053 ÷ 2 = 1 026 + 1;
- 1 026 ÷ 2 = 513 + 0;
- 513 ÷ 2 = 256 + 1;
- 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.
17 227 214 209(10) = 100 0000 0010 1101 0010 0110 1101 1000 0001(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 35.
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, 35,
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 17 227 214 209(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
17 227 214 209(10) = 0000 0000 0000 0000 0000 0000 0000 0100 0000 0010 1101 0010 0110 1101 1000 0001
Spaces were used to group digits: for binary, by 4, for decimal, by 3.