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;
- 241 164 ÷ 2 = 120 582 + 0;
- 120 582 ÷ 2 = 60 291 + 0;
- 60 291 ÷ 2 = 30 145 + 1;
- 30 145 ÷ 2 = 15 072 + 1;
- 15 072 ÷ 2 = 7 536 + 0;
- 7 536 ÷ 2 = 3 768 + 0;
- 3 768 ÷ 2 = 1 884 + 0;
- 1 884 ÷ 2 = 942 + 0;
- 942 ÷ 2 = 471 + 0;
- 471 ÷ 2 = 235 + 1;
- 235 ÷ 2 = 117 + 1;
- 117 ÷ 2 = 58 + 1;
- 58 ÷ 2 = 29 + 0;
- 29 ÷ 2 = 14 + 1;
- 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.
241 164(10) = 11 1010 1110 0000 1100(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 241 164(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
241 164(10) = 0000 0000 0000 0011 1010 1110 0000 1100
Spaces were used to group digits: for binary, by 4, for decimal, by 3.