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;
- 1 243 142 ÷ 2 = 621 571 + 0;
- 621 571 ÷ 2 = 310 785 + 1;
- 310 785 ÷ 2 = 155 392 + 1;
- 155 392 ÷ 2 = 77 696 + 0;
- 77 696 ÷ 2 = 38 848 + 0;
- 38 848 ÷ 2 = 19 424 + 0;
- 19 424 ÷ 2 = 9 712 + 0;
- 9 712 ÷ 2 = 4 856 + 0;
- 4 856 ÷ 2 = 2 428 + 0;
- 2 428 ÷ 2 = 1 214 + 0;
- 1 214 ÷ 2 = 607 + 0;
- 607 ÷ 2 = 303 + 1;
- 303 ÷ 2 = 151 + 1;
- 151 ÷ 2 = 75 + 1;
- 75 ÷ 2 = 37 + 1;
- 37 ÷ 2 = 18 + 1;
- 18 ÷ 2 = 9 + 0;
- 9 ÷ 2 = 4 + 1;
- 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.
1 243 142(10) = 1 0010 1111 1000 0000 0110(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 21.
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, 21,
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 1 243 142(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
1 243 142(10) = 0000 0000 0001 0010 1111 1000 0000 0110
Spaces were used to group digits: for binary, by 4, for decimal, by 3.