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;
- 1 065 353 217 ÷ 2 = 532 676 608 + 1;
- 532 676 608 ÷ 2 = 266 338 304 + 0;
- 266 338 304 ÷ 2 = 133 169 152 + 0;
- 133 169 152 ÷ 2 = 66 584 576 + 0;
- 66 584 576 ÷ 2 = 33 292 288 + 0;
- 33 292 288 ÷ 2 = 16 646 144 + 0;
- 16 646 144 ÷ 2 = 8 323 072 + 0;
- 8 323 072 ÷ 2 = 4 161 536 + 0;
- 4 161 536 ÷ 2 = 2 080 768 + 0;
- 2 080 768 ÷ 2 = 1 040 384 + 0;
- 1 040 384 ÷ 2 = 520 192 + 0;
- 520 192 ÷ 2 = 260 096 + 0;
- 260 096 ÷ 2 = 130 048 + 0;
- 130 048 ÷ 2 = 65 024 + 0;
- 65 024 ÷ 2 = 32 512 + 0;
- 32 512 ÷ 2 = 16 256 + 0;
- 16 256 ÷ 2 = 8 128 + 0;
- 8 128 ÷ 2 = 4 064 + 0;
- 4 064 ÷ 2 = 2 032 + 0;
- 2 032 ÷ 2 = 1 016 + 0;
- 1 016 ÷ 2 = 508 + 0;
- 508 ÷ 2 = 254 + 0;
- 254 ÷ 2 = 127 + 0;
- 127 ÷ 2 = 63 + 1;
- 63 ÷ 2 = 31 + 1;
- 31 ÷ 2 = 15 + 1;
- 15 ÷ 2 = 7 + 1;
- 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.
1 065 353 217(10) = 11 1111 1000 0000 0000 0000 0000 0001(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 30.
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, 30,
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 1 065 353 217(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:
1 065 353 217(10) = 0011 1111 1000 0000 0000 0000 0000 0001
Spaces were used to group digits: for binary, by 4, for decimal, by 3.