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;
- 767 180 753 ÷ 2 = 383 590 376 + 1;
- 383 590 376 ÷ 2 = 191 795 188 + 0;
- 191 795 188 ÷ 2 = 95 897 594 + 0;
- 95 897 594 ÷ 2 = 47 948 797 + 0;
- 47 948 797 ÷ 2 = 23 974 398 + 1;
- 23 974 398 ÷ 2 = 11 987 199 + 0;
- 11 987 199 ÷ 2 = 5 993 599 + 1;
- 5 993 599 ÷ 2 = 2 996 799 + 1;
- 2 996 799 ÷ 2 = 1 498 399 + 1;
- 1 498 399 ÷ 2 = 749 199 + 1;
- 749 199 ÷ 2 = 374 599 + 1;
- 374 599 ÷ 2 = 187 299 + 1;
- 187 299 ÷ 2 = 93 649 + 1;
- 93 649 ÷ 2 = 46 824 + 1;
- 46 824 ÷ 2 = 23 412 + 0;
- 23 412 ÷ 2 = 11 706 + 0;
- 11 706 ÷ 2 = 5 853 + 0;
- 5 853 ÷ 2 = 2 926 + 1;
- 2 926 ÷ 2 = 1 463 + 0;
- 1 463 ÷ 2 = 731 + 1;
- 731 ÷ 2 = 365 + 1;
- 365 ÷ 2 = 182 + 1;
- 182 ÷ 2 = 91 + 0;
- 91 ÷ 2 = 45 + 1;
- 45 ÷ 2 = 22 + 1;
- 22 ÷ 2 = 11 + 0;
- 11 ÷ 2 = 5 + 1;
- 5 ÷ 2 = 2 + 1;
- 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.
767 180 753(10) = 10 1101 1011 1010 0011 1111 1101 0001(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 30.
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, 30,
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 767 180 753(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
767 180 753(10) = 0010 1101 1011 1010 0011 1111 1101 0001
Spaces were used to group digits: for binary, by 4, for decimal, by 3.