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;
- 1 996 488 756 ÷ 2 = 998 244 378 + 0;
- 998 244 378 ÷ 2 = 499 122 189 + 0;
- 499 122 189 ÷ 2 = 249 561 094 + 1;
- 249 561 094 ÷ 2 = 124 780 547 + 0;
- 124 780 547 ÷ 2 = 62 390 273 + 1;
- 62 390 273 ÷ 2 = 31 195 136 + 1;
- 31 195 136 ÷ 2 = 15 597 568 + 0;
- 15 597 568 ÷ 2 = 7 798 784 + 0;
- 7 798 784 ÷ 2 = 3 899 392 + 0;
- 3 899 392 ÷ 2 = 1 949 696 + 0;
- 1 949 696 ÷ 2 = 974 848 + 0;
- 974 848 ÷ 2 = 487 424 + 0;
- 487 424 ÷ 2 = 243 712 + 0;
- 243 712 ÷ 2 = 121 856 + 0;
- 121 856 ÷ 2 = 60 928 + 0;
- 60 928 ÷ 2 = 30 464 + 0;
- 30 464 ÷ 2 = 15 232 + 0;
- 15 232 ÷ 2 = 7 616 + 0;
- 7 616 ÷ 2 = 3 808 + 0;
- 3 808 ÷ 2 = 1 904 + 0;
- 1 904 ÷ 2 = 952 + 0;
- 952 ÷ 2 = 476 + 0;
- 476 ÷ 2 = 238 + 0;
- 238 ÷ 2 = 119 + 0;
- 119 ÷ 2 = 59 + 1;
- 59 ÷ 2 = 29 + 1;
- 29 ÷ 2 = 14 + 1;
- 14 ÷ 2 = 7 + 0;
- 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.
1 996 488 756(10) = 111 0111 0000 0000 0000 0000 0011 0100(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 1 996 488 756(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:
1 996 488 756(10) = 0111 0111 0000 0000 0000 0000 0011 0100
Spaces were used to group digits: for binary, by 4, for decimal, by 3.