Discussion
Which one of the following is decimal value of a signed binary number 1101010, if it is in 2's complement form ?
Answer: B
The signed binary number 1101010 in 2's complement form has a leading 1, so it is negative. To find its magnitude, invert the bits to get 0010101 and add 1 to get 0010110, which is 16 + 4 + 2 = 22. So the value is -22, option (B). The value -42 in (A) is what is found by reading the number as a sign and magnitude, 1 followed by 101010 = 42, and -106 in (D) comes from taking the unsigned 1101010 = 106 and adding a negative sign. The value -21 in (C) results from inverting the bits without adding 1.
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