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;
- 234 375 ÷ 2 = 117 187 + 1;
- 117 187 ÷ 2 = 58 593 + 1;
- 58 593 ÷ 2 = 29 296 + 1;
- 29 296 ÷ 2 = 14 648 + 0;
- 14 648 ÷ 2 = 7 324 + 0;
- 7 324 ÷ 2 = 3 662 + 0;
- 3 662 ÷ 2 = 1 831 + 0;
- 1 831 ÷ 2 = 915 + 1;
- 915 ÷ 2 = 457 + 1;
- 457 ÷ 2 = 228 + 1;
- 228 ÷ 2 = 114 + 0;
- 114 ÷ 2 = 57 + 0;
- 57 ÷ 2 = 28 + 1;
- 28 ÷ 2 = 14 + 0;
- 14 ÷ 2 = 7 + 0;
- 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.
234 375(10) = 11 1001 0011 1000 0111(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 18.
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, 18,
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 234 375(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
234 375(10) = 0000 0000 0000 0011 1001 0011 1000 0111
Spaces were used to group digits: for binary, by 4, for decimal, by 3.