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;
- 1 990 057 ÷ 2 = 995 028 + 1;
- 995 028 ÷ 2 = 497 514 + 0;
- 497 514 ÷ 2 = 248 757 + 0;
- 248 757 ÷ 2 = 124 378 + 1;
- 124 378 ÷ 2 = 62 189 + 0;
- 62 189 ÷ 2 = 31 094 + 1;
- 31 094 ÷ 2 = 15 547 + 0;
- 15 547 ÷ 2 = 7 773 + 1;
- 7 773 ÷ 2 = 3 886 + 1;
- 3 886 ÷ 2 = 1 943 + 0;
- 1 943 ÷ 2 = 971 + 1;
- 971 ÷ 2 = 485 + 1;
- 485 ÷ 2 = 242 + 1;
- 242 ÷ 2 = 121 + 0;
- 121 ÷ 2 = 60 + 1;
- 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.
1 990 057(10) = 1 1110 0101 1101 1010 1001(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 21.
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, 21,
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 1 990 057(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
1 990 057(10) = 0000 0000 0001 1110 0101 1101 1010 1001
Spaces were used to group digits: for binary, by 4, for decimal, by 3.