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;
- 76 325 ÷ 2 = 38 162 + 1;
- 38 162 ÷ 2 = 19 081 + 0;
- 19 081 ÷ 2 = 9 540 + 1;
- 9 540 ÷ 2 = 4 770 + 0;
- 4 770 ÷ 2 = 2 385 + 0;
- 2 385 ÷ 2 = 1 192 + 1;
- 1 192 ÷ 2 = 596 + 0;
- 596 ÷ 2 = 298 + 0;
- 298 ÷ 2 = 149 + 0;
- 149 ÷ 2 = 74 + 1;
- 74 ÷ 2 = 37 + 0;
- 37 ÷ 2 = 18 + 1;
- 18 ÷ 2 = 9 + 0;
- 9 ÷ 2 = 4 + 1;
- 4 ÷ 2 = 2 + 0;
- 2 ÷ 2 = 1 + 0;
- 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.
76 325(10) = 1 0010 1010 0010 0101(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:
76 325(10) = 0000 0000 0000 0001 0010 1010 0010 0101
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 -76 325(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
-76 325(10) = 1000 0000 0000 0001 0010 1010 0010 0101
Spaces were used to group digits: for binary, by 4, for decimal, by 3.