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;
- 1 082 130 432 ÷ 2 = 541 065 216 + 0;
- 541 065 216 ÷ 2 = 270 532 608 + 0;
- 270 532 608 ÷ 2 = 135 266 304 + 0;
- 135 266 304 ÷ 2 = 67 633 152 + 0;
- 67 633 152 ÷ 2 = 33 816 576 + 0;
- 33 816 576 ÷ 2 = 16 908 288 + 0;
- 16 908 288 ÷ 2 = 8 454 144 + 0;
- 8 454 144 ÷ 2 = 4 227 072 + 0;
- 4 227 072 ÷ 2 = 2 113 536 + 0;
- 2 113 536 ÷ 2 = 1 056 768 + 0;
- 1 056 768 ÷ 2 = 528 384 + 0;
- 528 384 ÷ 2 = 264 192 + 0;
- 264 192 ÷ 2 = 132 096 + 0;
- 132 096 ÷ 2 = 66 048 + 0;
- 66 048 ÷ 2 = 33 024 + 0;
- 33 024 ÷ 2 = 16 512 + 0;
- 16 512 ÷ 2 = 8 256 + 0;
- 8 256 ÷ 2 = 4 128 + 0;
- 4 128 ÷ 2 = 2 064 + 0;
- 2 064 ÷ 2 = 1 032 + 0;
- 1 032 ÷ 2 = 516 + 0;
- 516 ÷ 2 = 258 + 0;
- 258 ÷ 2 = 129 + 0;
- 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.
1 082 130 432(10) = 100 0000 1000 0000 0000 0000 0000 0000(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 31.
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, 31,
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 1 082 130 432(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:
1 082 130 432(10) = 0100 0000 1000 0000 0000 0000 0000 0000
Spaces were used to group digits: for binary, by 4, for decimal, by 3.