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;
- 110 100 110 065 ÷ 2 = 55 050 055 032 + 1;
- 55 050 055 032 ÷ 2 = 27 525 027 516 + 0;
- 27 525 027 516 ÷ 2 = 13 762 513 758 + 0;
- 13 762 513 758 ÷ 2 = 6 881 256 879 + 0;
- 6 881 256 879 ÷ 2 = 3 440 628 439 + 1;
- 3 440 628 439 ÷ 2 = 1 720 314 219 + 1;
- 1 720 314 219 ÷ 2 = 860 157 109 + 1;
- 860 157 109 ÷ 2 = 430 078 554 + 1;
- 430 078 554 ÷ 2 = 215 039 277 + 0;
- 215 039 277 ÷ 2 = 107 519 638 + 1;
- 107 519 638 ÷ 2 = 53 759 819 + 0;
- 53 759 819 ÷ 2 = 26 879 909 + 1;
- 26 879 909 ÷ 2 = 13 439 954 + 1;
- 13 439 954 ÷ 2 = 6 719 977 + 0;
- 6 719 977 ÷ 2 = 3 359 988 + 1;
- 3 359 988 ÷ 2 = 1 679 994 + 0;
- 1 679 994 ÷ 2 = 839 997 + 0;
- 839 997 ÷ 2 = 419 998 + 1;
- 419 998 ÷ 2 = 209 999 + 0;
- 209 999 ÷ 2 = 104 999 + 1;
- 104 999 ÷ 2 = 52 499 + 1;
- 52 499 ÷ 2 = 26 249 + 1;
- 26 249 ÷ 2 = 13 124 + 1;
- 13 124 ÷ 2 = 6 562 + 0;
- 6 562 ÷ 2 = 3 281 + 0;
- 3 281 ÷ 2 = 1 640 + 1;
- 1 640 ÷ 2 = 820 + 0;
- 820 ÷ 2 = 410 + 0;
- 410 ÷ 2 = 205 + 0;
- 205 ÷ 2 = 102 + 1;
- 102 ÷ 2 = 51 + 0;
- 51 ÷ 2 = 25 + 1;
- 25 ÷ 2 = 12 + 1;
- 12 ÷ 2 = 6 + 0;
- 6 ÷ 2 = 3 + 0;
- 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.
110 100 110 065(10) = 1 1001 1010 0010 0111 1010 0101 1010 1111 0001(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 110 100 110 065(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:
110 100 110 065(10) = 0000 0000 0000 0000 0000 0000 0001 1001 1010 0010 0111 1010 0101 1010 1111 0001
Spaces were used to group digits: for binary, by 4, for decimal, by 3.