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;
- 990 971 ÷ 2 = 495 485 + 1;
- 495 485 ÷ 2 = 247 742 + 1;
- 247 742 ÷ 2 = 123 871 + 0;
- 123 871 ÷ 2 = 61 935 + 1;
- 61 935 ÷ 2 = 30 967 + 1;
- 30 967 ÷ 2 = 15 483 + 1;
- 15 483 ÷ 2 = 7 741 + 1;
- 7 741 ÷ 2 = 3 870 + 1;
- 3 870 ÷ 2 = 1 935 + 0;
- 1 935 ÷ 2 = 967 + 1;
- 967 ÷ 2 = 483 + 1;
- 483 ÷ 2 = 241 + 1;
- 241 ÷ 2 = 120 + 1;
- 120 ÷ 2 = 60 + 0;
- 60 ÷ 2 = 30 + 0;
- 30 ÷ 2 = 15 + 0;
- 15 ÷ 2 = 7 + 1;
- 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.
990 971(10) = 1111 0001 1110 1111 1011(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 20.
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, 20,
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 990 971(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
990 971(10) = 0000 0000 0000 1111 0001 1110 1111 1011
Spaces were used to group digits: for binary, by 4, for decimal, by 3.