Question

Represent the following integers in sign and magnitude form, 1's complement
2's complement form by using eight bits of (a) +25, (-30)123​

Answer 1

Explanation:

Positive Signed Binary Numbers

positive signed binary numbers

Negative Signed Binary Numbers

negative signed binary numbers

The disadvantage here is that whereas before we had a full range n-bit unsigned binary number, we now have an n-1 bit signed binary number giving a reduced range of digits from:

-2(n-1) to +2(n-1)

So for example: if we have 4 bits to represent a signed binary number, (1-bit for the Sign bit and 3-bits for the Magnitude bits), then the actual range of numbers we can represent in sign-magnitude notation would be:

-2(4-1) – 1 to +2(4-1) – 1

-2(3) – 1 to +2(3) – 1

-7 to +7