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;
- 543 216 839 ÷ 2 = 271 608 419 + 1;
- 271 608 419 ÷ 2 = 135 804 209 + 1;
- 135 804 209 ÷ 2 = 67 902 104 + 1;
- 67 902 104 ÷ 2 = 33 951 052 + 0;
- 33 951 052 ÷ 2 = 16 975 526 + 0;
- 16 975 526 ÷ 2 = 8 487 763 + 0;
- 8 487 763 ÷ 2 = 4 243 881 + 1;
- 4 243 881 ÷ 2 = 2 121 940 + 1;
- 2 121 940 ÷ 2 = 1 060 970 + 0;
- 1 060 970 ÷ 2 = 530 485 + 0;
- 530 485 ÷ 2 = 265 242 + 1;
- 265 242 ÷ 2 = 132 621 + 0;
- 132 621 ÷ 2 = 66 310 + 1;
- 66 310 ÷ 2 = 33 155 + 0;
- 33 155 ÷ 2 = 16 577 + 1;
- 16 577 ÷ 2 = 8 288 + 1;
- 8 288 ÷ 2 = 4 144 + 0;
- 4 144 ÷ 2 = 2 072 + 0;
- 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.
543 216 839(10) = 10 0000 0110 0000 1101 0100 1100 0111(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) is reserved for 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 543 216 839(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
543 216 839(10) = 0010 0000 0110 0000 1101 0100 1100 0111
Spaces were used to group digits: for binary, by 4, for decimal, by 3.