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;
- 3 600 294 ÷ 2 = 1 800 147 + 0;
- 1 800 147 ÷ 2 = 900 073 + 1;
- 900 073 ÷ 2 = 450 036 + 1;
- 450 036 ÷ 2 = 225 018 + 0;
- 225 018 ÷ 2 = 112 509 + 0;
- 112 509 ÷ 2 = 56 254 + 1;
- 56 254 ÷ 2 = 28 127 + 0;
- 28 127 ÷ 2 = 14 063 + 1;
- 14 063 ÷ 2 = 7 031 + 1;
- 7 031 ÷ 2 = 3 515 + 1;
- 3 515 ÷ 2 = 1 757 + 1;
- 1 757 ÷ 2 = 878 + 1;
- 878 ÷ 2 = 439 + 0;
- 439 ÷ 2 = 219 + 1;
- 219 ÷ 2 = 109 + 1;
- 109 ÷ 2 = 54 + 1;
- 54 ÷ 2 = 27 + 0;
- 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.
3 600 294(10) = 11 0110 1110 1111 1010 0110(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 22.
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, 22,
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 3 600 294(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:
3 600 294(10) = 0000 0000 0011 0110 1110 1111 1010 0110
Spaces were used to group digits: for binary, by 4, for decimal, by 3.