1· (32 points) Negate the following binary numbers in 6-bit 2\'s complement repr

Question

1· (32 points) Negate the following binary numbers in 6-bit 2's complement representation a) (8 points) 0010102 b) (8 points) 1100112 c) (8 points) 1001002 d) (8 points) 0100012 2. (40 points) Give the 5-bit 2's complement representation for the following decimal numbers: a) (10 points) -15 b) (10 points) -10 c) (10 points) 0 d) (10 points) 7 3. (28 points) What is the value represented by the bit string 110101 if: a) (8 points) it is in sign-and-magnitude representation? b) (10 points) it is in 1's complement representation? c) (10 points) it is in 2's complement representation?

Explanation / Answer

Q1.

2’s complement is flipping the bits and adding one.

a). flip(001010) + 1 = 110101 + 1 = (110110)2

b). flip(110011) + 1 = 001100 + 1 = (001101)2

c). flip(100100) + 1 = 011011 + 1 = (011100)2

d). flip(010001) + 1 = 101110 + 1 = (101111)2

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