Which one of the following statements is true?

a. In one's complement format, the leftmost bit is saved for the sign where 1 indicates a negative number and 0 indicates a positive number.

b. The smallest integer that can be represented by a sign-and-magnitude binary number is always 0.

c. It is impossible to store 1610 in 4-bits because overflow will occur. d. The two's complement representation of + 6710 in 8-bits is 1000011.

a. In one's complement format, the leftmost bit is saved for the sign where 1 indicates a negative number and 0 indicates a positive number.

Explanation:

In binary numbers, 1's complement is used to represent the signed binary numbers. In unsigned numbers, there is no need of sign. But in signed binary numbers a signed bit is required. To add the bit that is represent the sign of the number in binary, 0 represents the positive number while 1 represents the negative number.

If we have a number and want to convert it in signed binary number, we just takes it 1's complement and add the signed bit at the left of the number.

E. g.

1 = 0001

is the binary of 1, if we want to add sign, we just add the zero at left most side of the binary which make it positive as given below:

+1 = 0 0001

Now of we want to convert it into negative than, we take 1's complement in which all bits are inverted.

-1 = 1 1110