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;
- 195 090 320 ÷ 2 = 97 545 160 + 0;
- 97 545 160 ÷ 2 = 48 772 580 + 0;
- 48 772 580 ÷ 2 = 24 386 290 + 0;
- 24 386 290 ÷ 2 = 12 193 145 + 0;
- 12 193 145 ÷ 2 = 6 096 572 + 1;
- 6 096 572 ÷ 2 = 3 048 286 + 0;
- 3 048 286 ÷ 2 = 1 524 143 + 0;
- 1 524 143 ÷ 2 = 762 071 + 1;
- 762 071 ÷ 2 = 381 035 + 1;
- 381 035 ÷ 2 = 190 517 + 1;
- 190 517 ÷ 2 = 95 258 + 1;
- 95 258 ÷ 2 = 47 629 + 0;
- 47 629 ÷ 2 = 23 814 + 1;
- 23 814 ÷ 2 = 11 907 + 0;
- 11 907 ÷ 2 = 5 953 + 1;
- 5 953 ÷ 2 = 2 976 + 1;
- 2 976 ÷ 2 = 1 488 + 0;
- 1 488 ÷ 2 = 744 + 0;
- 744 ÷ 2 = 372 + 0;
- 372 ÷ 2 = 186 + 0;
- 186 ÷ 2 = 93 + 0;
- 93 ÷ 2 = 46 + 1;
- 46 ÷ 2 = 23 + 0;
- 23 ÷ 2 = 11 + 1;
- 11 ÷ 2 = 5 + 1;
- 5 ÷ 2 = 2 + 1;
- 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.
195 090 320(10) = 1011 1010 0000 1101 0111 1001 0000(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 28.
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, 28,
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 195 090 320(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
195 090 320(10) = 0000 1011 1010 0000 1101 0111 1001 0000
Spaces were used to group digits: for binary, by 4, for decimal, by 3.