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;
- 717 359 131 ÷ 2 = 358 679 565 + 1;
- 358 679 565 ÷ 2 = 179 339 782 + 1;
- 179 339 782 ÷ 2 = 89 669 891 + 0;
- 89 669 891 ÷ 2 = 44 834 945 + 1;
- 44 834 945 ÷ 2 = 22 417 472 + 1;
- 22 417 472 ÷ 2 = 11 208 736 + 0;
- 11 208 736 ÷ 2 = 5 604 368 + 0;
- 5 604 368 ÷ 2 = 2 802 184 + 0;
- 2 802 184 ÷ 2 = 1 401 092 + 0;
- 1 401 092 ÷ 2 = 700 546 + 0;
- 700 546 ÷ 2 = 350 273 + 0;
- 350 273 ÷ 2 = 175 136 + 1;
- 175 136 ÷ 2 = 87 568 + 0;
- 87 568 ÷ 2 = 43 784 + 0;
- 43 784 ÷ 2 = 21 892 + 0;
- 21 892 ÷ 2 = 10 946 + 0;
- 10 946 ÷ 2 = 5 473 + 0;
- 5 473 ÷ 2 = 2 736 + 1;
- 2 736 ÷ 2 = 1 368 + 0;
- 1 368 ÷ 2 = 684 + 0;
- 684 ÷ 2 = 342 + 0;
- 342 ÷ 2 = 171 + 0;
- 171 ÷ 2 = 85 + 1;
- 85 ÷ 2 = 42 + 1;
- 42 ÷ 2 = 21 + 0;
- 21 ÷ 2 = 10 + 1;
- 10 ÷ 2 = 5 + 0;
- 5 ÷ 2 = 2 + 1;
- 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.
717 359 131(10) = 10 1010 1100 0010 0000 1000 0001 1011(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 717 359 131(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:
717 359 131(10) = 0010 1010 1100 0010 0000 1000 0001 1011
Spaces were used to group digits: for binary, by 4, for decimal, by 3.