25.02to binary:
Integer Part:
1 x 16 = 0
1 x 8 = 8
0 x 4 = 0
0 x 2 = 0
1 x 1 = 1
Total: 25
11001
Fractional Part:
0.020 x 2 = 0.400 = 0
0.00 x 2 = 0.00 = 0
0.0 x 2 = 0.0 = 0
25.02 decimal is11001.000 binary.
11001.000 binary to hexadecimal:
1 0 0 1
______
8 4 2 1
8 + 0 + 0 + 1 = 9
0 0 0 1
______
8 4 2 1
0 + 0 + 0 + 1 = 1
19 hexadecimal
Fractional portion is zero in binary.
IEEE 754 binary = 01000001110010000010100011110110
First number: 18
Second number: -4
18 decimal:
0 0 0 1 0 0 1 0
______
128 64 32 16 8 4 2 1
-4 decimal:
First, take 4 decimal
0 0 0 0 0 1 0 0
______
128 64 32 16 8 4 2 1
Then, take 2’s complement:
1 1 1 1 1 1 0 0
Add them together:
0 0 1 0 0 1 0
1 1 1 1 1 0 0
------
0 0 0 0 1 1 1 0
If a computer can only store and manipulate integers, that means it can’t handle floating point numbers. It could store the number 89, but it couldn’t store the number 89.25. Every number with a fractional portion would lose its fractional portion when the computer handled it. This would cause all kinds of problems. It couldn’t be used to calculate change due or for scientific, accounting or most math purposes.
The way you could overcome it would be to take the floating point number and multiply it by 100 to be able to store two decimal places, but as integers to the left of the decimal point. There would be a rule that says every number is stored in the system as that number times 100. For example, 67 would be stored as 6700, and 71.25 would be stored as 7125.