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;
- 7 516 897 ÷ 2 = 3 758 448 + 1;
- 3 758 448 ÷ 2 = 1 879 224 + 0;
- 1 879 224 ÷ 2 = 939 612 + 0;
- 939 612 ÷ 2 = 469 806 + 0;
- 469 806 ÷ 2 = 234 903 + 0;
- 234 903 ÷ 2 = 117 451 + 1;
- 117 451 ÷ 2 = 58 725 + 1;
- 58 725 ÷ 2 = 29 362 + 1;
- 29 362 ÷ 2 = 14 681 + 0;
- 14 681 ÷ 2 = 7 340 + 1;
- 7 340 ÷ 2 = 3 670 + 0;
- 3 670 ÷ 2 = 1 835 + 0;
- 1 835 ÷ 2 = 917 + 1;
- 917 ÷ 2 = 458 + 1;
- 458 ÷ 2 = 229 + 0;
- 229 ÷ 2 = 114 + 1;
- 114 ÷ 2 = 57 + 0;
- 57 ÷ 2 = 28 + 1;
- 28 ÷ 2 = 14 + 0;
- 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.
7 516 897(10) = 111 0010 1011 0010 1110 0001(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 23.
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, 23,
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 7 516 897(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:
7 516 897(10) = 0000 0000 0111 0010 1011 0010 1110 0001
Spaces were used to group digits: for binary, by 4, for decimal, by 3.