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;
- 1 515 516 ÷ 2 = 757 758 + 0;
- 757 758 ÷ 2 = 378 879 + 0;
- 378 879 ÷ 2 = 189 439 + 1;
- 189 439 ÷ 2 = 94 719 + 1;
- 94 719 ÷ 2 = 47 359 + 1;
- 47 359 ÷ 2 = 23 679 + 1;
- 23 679 ÷ 2 = 11 839 + 1;
- 11 839 ÷ 2 = 5 919 + 1;
- 5 919 ÷ 2 = 2 959 + 1;
- 2 959 ÷ 2 = 1 479 + 1;
- 1 479 ÷ 2 = 739 + 1;
- 739 ÷ 2 = 369 + 1;
- 369 ÷ 2 = 184 + 1;
- 184 ÷ 2 = 92 + 0;
- 92 ÷ 2 = 46 + 0;
- 46 ÷ 2 = 23 + 0;
- 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.
1 515 516(10) = 1 0111 0001 1111 1111 1100(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 21.
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, 21,
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 1 515 516(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:
1 515 516(10) = 0000 0000 0001 0111 0001 1111 1111 1100
Spaces were used to group digits: for binary, by 4, for decimal, by 3.