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;
- 1 010 001 101 ÷ 2 = 505 000 550 + 1;
- 505 000 550 ÷ 2 = 252 500 275 + 0;
- 252 500 275 ÷ 2 = 126 250 137 + 1;
- 126 250 137 ÷ 2 = 63 125 068 + 1;
- 63 125 068 ÷ 2 = 31 562 534 + 0;
- 31 562 534 ÷ 2 = 15 781 267 + 0;
- 15 781 267 ÷ 2 = 7 890 633 + 1;
- 7 890 633 ÷ 2 = 3 945 316 + 1;
- 3 945 316 ÷ 2 = 1 972 658 + 0;
- 1 972 658 ÷ 2 = 986 329 + 0;
- 986 329 ÷ 2 = 493 164 + 1;
- 493 164 ÷ 2 = 246 582 + 0;
- 246 582 ÷ 2 = 123 291 + 0;
- 123 291 ÷ 2 = 61 645 + 1;
- 61 645 ÷ 2 = 30 822 + 1;
- 30 822 ÷ 2 = 15 411 + 0;
- 15 411 ÷ 2 = 7 705 + 1;
- 7 705 ÷ 2 = 3 852 + 1;
- 3 852 ÷ 2 = 1 926 + 0;
- 1 926 ÷ 2 = 963 + 0;
- 963 ÷ 2 = 481 + 1;
- 481 ÷ 2 = 240 + 1;
- 240 ÷ 2 = 120 + 0;
- 120 ÷ 2 = 60 + 0;
- 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.
1 010 001 101(10) = 11 1100 0011 0011 0110 0100 1100 1101(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 1 010 001 101(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:
1 010 001 101(10) = 0011 1100 0011 0011 0110 0100 1100 1101
Spaces were used to group digits: for binary, by 4, for decimal, by 3.