Question

1.Given that you are working with a 3-bit 2's complement system. What is the additive inverse of -4? That is, -4 + ? = 0 (zero).

2.What is the 7-bit 1's complement representation of 1010101₂

_3.What is the 6-bit sign-magnitude representation of 100101₂?

answer in decimal

Answer 1

1)
-4 in 2's complement is 100
it's additive inverse is 4.
it can't be stored inside a 3-bit 2's complement.
so, inverse can not be stored inside a 3-bit 2's complement.

2)
since left most bit is 1, this number is negative number.
so, follow these steps below to convert this into a decimal value.
first flip all the bits. Flip all 0's to 1 and all 1's to 0.
   1010101 is flipped to 0101010
Now convert this result(0101010) to decimal value
=> 0101010
=> 0x2^6+1x2^5+0x2^4+1x2^3+0x2^2+1x2^1+0x2^0
=> 0x64+1x32+0x16+1x8+0x4+1x2+0x1
=> 0+32+0+8+0+2+0
=> 42
Answer: -42

3)
since left most bit is 1, this number is negative number.
00101
Now convert 00101 to decimal value
=> 00101
=> 0x2^4+0x2^3+1x2^2+0x2^1+1x2^0
=> 0x16+0x8+1x4+0x2+1x1
=> 0+0+4+0+1
=> 5
Answer: -5