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;
- 61 274 937 ÷ 2 = 30 637 468 + 1;
- 30 637 468 ÷ 2 = 15 318 734 + 0;
- 15 318 734 ÷ 2 = 7 659 367 + 0;
- 7 659 367 ÷ 2 = 3 829 683 + 1;
- 3 829 683 ÷ 2 = 1 914 841 + 1;
- 1 914 841 ÷ 2 = 957 420 + 1;
- 957 420 ÷ 2 = 478 710 + 0;
- 478 710 ÷ 2 = 239 355 + 0;
- 239 355 ÷ 2 = 119 677 + 1;
- 119 677 ÷ 2 = 59 838 + 1;
- 59 838 ÷ 2 = 29 919 + 0;
- 29 919 ÷ 2 = 14 959 + 1;
- 14 959 ÷ 2 = 7 479 + 1;
- 7 479 ÷ 2 = 3 739 + 1;
- 3 739 ÷ 2 = 1 869 + 1;
- 1 869 ÷ 2 = 934 + 1;
- 934 ÷ 2 = 467 + 0;
- 467 ÷ 2 = 233 + 1;
- 233 ÷ 2 = 116 + 1;
- 116 ÷ 2 = 58 + 0;
- 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.
61 274 937(10) = 11 1010 0110 1111 1011 0011 1001(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 26.
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, 26,
3) so that the first bit (leftmost) could be zero
(we deal with a positive number at this moment)
=== is: 32.
4. Get the positive binary computer representation on 32 bits (4 Bytes):
If needed, add extra 0s in front (to the left) of the base 2 number, up to the required length, 32.
Number 61 274 937(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:
61 274 937(10) = 0000 0011 1010 0110 1111 1011 0011 1001
Spaces were used to group digits: for binary, by 4, for decimal, by 3.