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;
- 946 465 012 ÷ 2 = 473 232 506 + 0;
- 473 232 506 ÷ 2 = 236 616 253 + 0;
- 236 616 253 ÷ 2 = 118 308 126 + 1;
- 118 308 126 ÷ 2 = 59 154 063 + 0;
- 59 154 063 ÷ 2 = 29 577 031 + 1;
- 29 577 031 ÷ 2 = 14 788 515 + 1;
- 14 788 515 ÷ 2 = 7 394 257 + 1;
- 7 394 257 ÷ 2 = 3 697 128 + 1;
- 3 697 128 ÷ 2 = 1 848 564 + 0;
- 1 848 564 ÷ 2 = 924 282 + 0;
- 924 282 ÷ 2 = 462 141 + 0;
- 462 141 ÷ 2 = 231 070 + 1;
- 231 070 ÷ 2 = 115 535 + 0;
- 115 535 ÷ 2 = 57 767 + 1;
- 57 767 ÷ 2 = 28 883 + 1;
- 28 883 ÷ 2 = 14 441 + 1;
- 14 441 ÷ 2 = 7 220 + 1;
- 7 220 ÷ 2 = 3 610 + 0;
- 3 610 ÷ 2 = 1 805 + 0;
- 1 805 ÷ 2 = 902 + 1;
- 902 ÷ 2 = 451 + 0;
- 451 ÷ 2 = 225 + 1;
- 225 ÷ 2 = 112 + 1;
- 112 ÷ 2 = 56 + 0;
- 56 ÷ 2 = 28 + 0;
- 28 ÷ 2 = 14 + 0;
- 14 ÷ 2 = 7 + 0;
- 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.
946 465 012(10) = 11 1000 0110 1001 1110 1000 1111 0100(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) indicates 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 946 465 012(10), a signed integer number (with sign), converted from decimal system (from base 10) and written as a signed binary in two's complement representation:
946 465 012(10) = 0011 1000 0110 1001 1110 1000 1111 0100
Spaces were used to group digits: for binary, by 4, for decimal, by 3.