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;
- 300 000 024 ÷ 2 = 150 000 012 + 0;
- 150 000 012 ÷ 2 = 75 000 006 + 0;
- 75 000 006 ÷ 2 = 37 500 003 + 0;
- 37 500 003 ÷ 2 = 18 750 001 + 1;
- 18 750 001 ÷ 2 = 9 375 000 + 1;
- 9 375 000 ÷ 2 = 4 687 500 + 0;
- 4 687 500 ÷ 2 = 2 343 750 + 0;
- 2 343 750 ÷ 2 = 1 171 875 + 0;
- 1 171 875 ÷ 2 = 585 937 + 1;
- 585 937 ÷ 2 = 292 968 + 1;
- 292 968 ÷ 2 = 146 484 + 0;
- 146 484 ÷ 2 = 73 242 + 0;
- 73 242 ÷ 2 = 36 621 + 0;
- 36 621 ÷ 2 = 18 310 + 1;
- 18 310 ÷ 2 = 9 155 + 0;
- 9 155 ÷ 2 = 4 577 + 1;
- 4 577 ÷ 2 = 2 288 + 1;
- 2 288 ÷ 2 = 1 144 + 0;
- 1 144 ÷ 2 = 572 + 0;
- 572 ÷ 2 = 286 + 0;
- 286 ÷ 2 = 143 + 0;
- 143 ÷ 2 = 71 + 1;
- 71 ÷ 2 = 35 + 1;
- 35 ÷ 2 = 17 + 1;
- 17 ÷ 2 = 8 + 1;
- 8 ÷ 2 = 4 + 0;
- 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.
300 000 024(10) = 1 0001 1110 0001 1010 0011 0001 1000(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 29.
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, 29,
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 300 000 024(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
300 000 024(10) = 0001 0001 1110 0001 1010 0011 0001 1000
Spaces were used to group digits: for binary, by 4, for decimal, by 3.