2. 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;
- 247 493 653 ÷ 2 = 123 746 826 + 1;
- 123 746 826 ÷ 2 = 61 873 413 + 0;
- 61 873 413 ÷ 2 = 30 936 706 + 1;
- 30 936 706 ÷ 2 = 15 468 353 + 0;
- 15 468 353 ÷ 2 = 7 734 176 + 1;
- 7 734 176 ÷ 2 = 3 867 088 + 0;
- 3 867 088 ÷ 2 = 1 933 544 + 0;
- 1 933 544 ÷ 2 = 966 772 + 0;
- 966 772 ÷ 2 = 483 386 + 0;
- 483 386 ÷ 2 = 241 693 + 0;
- 241 693 ÷ 2 = 120 846 + 1;
- 120 846 ÷ 2 = 60 423 + 0;
- 60 423 ÷ 2 = 30 211 + 1;
- 30 211 ÷ 2 = 15 105 + 1;
- 15 105 ÷ 2 = 7 552 + 1;
- 7 552 ÷ 2 = 3 776 + 0;
- 3 776 ÷ 2 = 1 888 + 0;
- 1 888 ÷ 2 = 944 + 0;
- 944 ÷ 2 = 472 + 0;
- 472 ÷ 2 = 236 + 0;
- 236 ÷ 2 = 118 + 0;
- 118 ÷ 2 = 59 + 0;
- 59 ÷ 2 = 29 + 1;
- 29 ÷ 2 = 14 + 1;
- 14 ÷ 2 = 7 + 0;
- 7 ÷ 2 = 3 + 1;
- 3 ÷ 2 = 1 + 1;
- 1 ÷ 2 = 0 + 1;
3. Construct the base 2 representation of the positive number:
Take all the remainders starting from the bottom of the list constructed above.
247 493 653(10) = 1110 1100 0000 0111 0100 0001 0101(2)
4. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 28.
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, 28,
3) so that the first bit (leftmost) could be zero
(we deal with a positive number at this moment)
=== is: 32.
5. 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:
247 493 653(10) = 0000 1110 1100 0000 0111 0100 0001 0101
6. Get the negative integer number representation:
To get the negative integer number representation on 32 bits (4 Bytes),
... change the first bit (the leftmost), from 0 to 1...
Number -247 493 653(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
-247 493 653(10) = 1000 1110 1100 0000 0111 0100 0001 0101
Spaces were used to group digits: for binary, by 4, for decimal, by 3.