Instructions: Convert these decimal numbers to 5-bit 2's-complement form, if possible. If not possible, explain why this is so.
(16) base 10
According to the online converter:
From what I understand,
If decimal is positive:
- STEP 1: Convert magnitude to binary.
- STEP 2: Pad 0's to desired bitsize.
If decimal is negative:
- STEP 1: Convert magnitude to binary.
- STEP 2: Pad 0's to desired bitsize.
- STEP 3: Invert bits to achieve 1's-complement.
- STEP 4: Add 1 to achieve 2's-complement.
Since 16 is positive, I simply converted it to binary by repeated division yielding (10000) base 2.
I no longer padded 0's since it is already 5-bits (containing 5 digits).
Can somebody explain to me why the online converter is returning an error (which also I strongly believe is the correct answer)?
Best Answer
With 5 bits you can represent up to 2^5 different numbers, since you want negative and positive numbers the range is -16 to +15.
so you get error since 16 is out of the range for 5 bits. Change to 6 bits and it should work