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;
- 20 121 964 ÷ 2 = 10 060 982 + 0;
- 10 060 982 ÷ 2 = 5 030 491 + 0;
- 5 030 491 ÷ 2 = 2 515 245 + 1;
- 2 515 245 ÷ 2 = 1 257 622 + 1;
- 1 257 622 ÷ 2 = 628 811 + 0;
- 628 811 ÷ 2 = 314 405 + 1;
- 314 405 ÷ 2 = 157 202 + 1;
- 157 202 ÷ 2 = 78 601 + 0;
- 78 601 ÷ 2 = 39 300 + 1;
- 39 300 ÷ 2 = 19 650 + 0;
- 19 650 ÷ 2 = 9 825 + 0;
- 9 825 ÷ 2 = 4 912 + 1;
- 4 912 ÷ 2 = 2 456 + 0;
- 2 456 ÷ 2 = 1 228 + 0;
- 1 228 ÷ 2 = 614 + 0;
- 614 ÷ 2 = 307 + 0;
- 307 ÷ 2 = 153 + 1;
- 153 ÷ 2 = 76 + 1;
- 76 ÷ 2 = 38 + 0;
- 38 ÷ 2 = 19 + 0;
- 19 ÷ 2 = 9 + 1;
- 9 ÷ 2 = 4 + 1;
- 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.
20 121 964(10) = 1 0011 0011 0000 1001 0110 1100(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 25.
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, 25,
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 20 121 964(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
20 121 964(10) = 0000 0001 0011 0011 0000 1001 0110 1100
Spaces were used to group digits: for binary, by 4, for decimal, by 3.