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;
- 193 003 556 ÷ 2 = 96 501 778 + 0;
- 96 501 778 ÷ 2 = 48 250 889 + 0;
- 48 250 889 ÷ 2 = 24 125 444 + 1;
- 24 125 444 ÷ 2 = 12 062 722 + 0;
- 12 062 722 ÷ 2 = 6 031 361 + 0;
- 6 031 361 ÷ 2 = 3 015 680 + 1;
- 3 015 680 ÷ 2 = 1 507 840 + 0;
- 1 507 840 ÷ 2 = 753 920 + 0;
- 753 920 ÷ 2 = 376 960 + 0;
- 376 960 ÷ 2 = 188 480 + 0;
- 188 480 ÷ 2 = 94 240 + 0;
- 94 240 ÷ 2 = 47 120 + 0;
- 47 120 ÷ 2 = 23 560 + 0;
- 23 560 ÷ 2 = 11 780 + 0;
- 11 780 ÷ 2 = 5 890 + 0;
- 5 890 ÷ 2 = 2 945 + 0;
- 2 945 ÷ 2 = 1 472 + 1;
- 1 472 ÷ 2 = 736 + 0;
- 736 ÷ 2 = 368 + 0;
- 368 ÷ 2 = 184 + 0;
- 184 ÷ 2 = 92 + 0;
- 92 ÷ 2 = 46 + 0;
- 46 ÷ 2 = 23 + 0;
- 23 ÷ 2 = 11 + 1;
- 11 ÷ 2 = 5 + 1;
- 5 ÷ 2 = 2 + 1;
- 2 ÷ 2 = 1 + 0;
- 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.
193 003 556(10) = 1011 1000 0001 0000 0000 0010 0100(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:
193 003 556(10) = 0000 1011 1000 0001 0000 0000 0010 0100
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 -193 003 556(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
-193 003 556(10) = 1000 1011 1000 0001 0000 0000 0010 0100
Spaces were used to group digits: for binary, by 4, for decimal, by 3.