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;
- 654 785 134 ÷ 2 = 327 392 567 + 0;
- 327 392 567 ÷ 2 = 163 696 283 + 1;
- 163 696 283 ÷ 2 = 81 848 141 + 1;
- 81 848 141 ÷ 2 = 40 924 070 + 1;
- 40 924 070 ÷ 2 = 20 462 035 + 0;
- 20 462 035 ÷ 2 = 10 231 017 + 1;
- 10 231 017 ÷ 2 = 5 115 508 + 1;
- 5 115 508 ÷ 2 = 2 557 754 + 0;
- 2 557 754 ÷ 2 = 1 278 877 + 0;
- 1 278 877 ÷ 2 = 639 438 + 1;
- 639 438 ÷ 2 = 319 719 + 0;
- 319 719 ÷ 2 = 159 859 + 1;
- 159 859 ÷ 2 = 79 929 + 1;
- 79 929 ÷ 2 = 39 964 + 1;
- 39 964 ÷ 2 = 19 982 + 0;
- 19 982 ÷ 2 = 9 991 + 0;
- 9 991 ÷ 2 = 4 995 + 1;
- 4 995 ÷ 2 = 2 497 + 1;
- 2 497 ÷ 2 = 1 248 + 1;
- 1 248 ÷ 2 = 624 + 0;
- 624 ÷ 2 = 312 + 0;
- 312 ÷ 2 = 156 + 0;
- 156 ÷ 2 = 78 + 0;
- 78 ÷ 2 = 39 + 0;
- 39 ÷ 2 = 19 + 1;
- 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.
654 785 134(10) = 10 0111 0000 0111 0011 1010 0110 1110(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 654 785 134(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
654 785 134(10) = 0010 0111 0000 0111 0011 1010 0110 1110
Spaces were used to group digits: for binary, by 4, for decimal, by 3.