The Essentials Of Computer Organization And Architecture 4th Edition by Linda Null,Julia Lobur

Exercise 110

Suppose we have just found yet another representation for floating-point numbers. Using this representation, a 12-bit floating-point number has 1 bit for the sign of the number, 4 bits for the exponent, and 7 bits for the mantissa, which is normalized as in the Simple Model so that the first digit to the right of the radix points must be a 1. Numbers in the exponent are in signed two's complement representation. No bias is used, and there are no implied bits. Show the representation for the smallest positive number this machine can represent using the following format (simply fill in the squares provided). What decimal number does this equate to?