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;
- 29 101 974 ÷ 2 = 14 550 987 + 0;
- 14 550 987 ÷ 2 = 7 275 493 + 1;
- 7 275 493 ÷ 2 = 3 637 746 + 1;
- 3 637 746 ÷ 2 = 1 818 873 + 0;
- 1 818 873 ÷ 2 = 909 436 + 1;
- 909 436 ÷ 2 = 454 718 + 0;
- 454 718 ÷ 2 = 227 359 + 0;
- 227 359 ÷ 2 = 113 679 + 1;
- 113 679 ÷ 2 = 56 839 + 1;
- 56 839 ÷ 2 = 28 419 + 1;
- 28 419 ÷ 2 = 14 209 + 1;
- 14 209 ÷ 2 = 7 104 + 1;
- 7 104 ÷ 2 = 3 552 + 0;
- 3 552 ÷ 2 = 1 776 + 0;
- 1 776 ÷ 2 = 888 + 0;
- 888 ÷ 2 = 444 + 0;
- 444 ÷ 2 = 222 + 0;
- 222 ÷ 2 = 111 + 0;
- 111 ÷ 2 = 55 + 1;
- 55 ÷ 2 = 27 + 1;
- 27 ÷ 2 = 13 + 1;
- 13 ÷ 2 = 6 + 1;
- 6 ÷ 2 = 3 + 0;
- 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.
29 101 974(10) = 1 1011 1100 0000 1111 1001 0110(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 25.
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, 25,
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 29 101 974(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:
29 101 974(10) = 0000 0001 1011 1100 0000 1111 1001 0110
Spaces were used to group digits: for binary, by 4, for decimal, by 3.