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;
- 8 489 919 ÷ 2 = 4 244 959 + 1;
- 4 244 959 ÷ 2 = 2 122 479 + 1;
- 2 122 479 ÷ 2 = 1 061 239 + 1;
- 1 061 239 ÷ 2 = 530 619 + 1;
- 530 619 ÷ 2 = 265 309 + 1;
- 265 309 ÷ 2 = 132 654 + 1;
- 132 654 ÷ 2 = 66 327 + 0;
- 66 327 ÷ 2 = 33 163 + 1;
- 33 163 ÷ 2 = 16 581 + 1;
- 16 581 ÷ 2 = 8 290 + 1;
- 8 290 ÷ 2 = 4 145 + 0;
- 4 145 ÷ 2 = 2 072 + 1;
- 2 072 ÷ 2 = 1 036 + 0;
- 1 036 ÷ 2 = 518 + 0;
- 518 ÷ 2 = 259 + 0;
- 259 ÷ 2 = 129 + 1;
- 129 ÷ 2 = 64 + 1;
- 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.
8 489 919(10) = 1000 0001 1000 1011 1011 1111(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 24.
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, 24,
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 8 489 919(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:
8 489 919(10) = 0000 0000 1000 0001 1000 1011 1011 1111
Spaces were used to group digits: for binary, by 4, for decimal, by 3.