2. 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;
- 123 122 ÷ 2 = 61 561 + 0;
- 61 561 ÷ 2 = 30 780 + 1;
- 30 780 ÷ 2 = 15 390 + 0;
- 15 390 ÷ 2 = 7 695 + 0;
- 7 695 ÷ 2 = 3 847 + 1;
- 3 847 ÷ 2 = 1 923 + 1;
- 1 923 ÷ 2 = 961 + 1;
- 961 ÷ 2 = 480 + 1;
- 480 ÷ 2 = 240 + 0;
- 240 ÷ 2 = 120 + 0;
- 120 ÷ 2 = 60 + 0;
- 60 ÷ 2 = 30 + 0;
- 30 ÷ 2 = 15 + 0;
- 15 ÷ 2 = 7 + 1;
- 7 ÷ 2 = 3 + 1;
- 3 ÷ 2 = 1 + 1;
- 1 ÷ 2 = 0 + 1;
3. Construct the base 2 representation of the positive number:
Take all the remainders starting from the bottom of the list constructed above.
123 122(10) = 1 1110 0000 1111 0010(2)
4. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 17.
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, 17,
3) so that the first bit (leftmost) could be zero
(we deal with a positive number at this moment)
=== is: 32.
5. 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:
123 122(10) = 0000 0000 0000 0001 1110 0000 1111 0010
6. Get the negative integer number representation:
To get the negative integer number representation on 32 bits (4 Bytes),
... change the first bit (the leftmost), from 0 to 1...
Number -123 122(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
-123 122(10) = 1000 0000 0000 0001 1110 0000 1111 0010
Spaces were used to group digits: for binary, by 4, for decimal, by 3.