Help: Floating Point Exam Question

The exponent in floating-point arithmetic doesn't use two's complement, instead, the exponent is already negative-biased. Therefore unlike two's complement, the smallest possible negative exponent is represented by all-zeroes in binary.

So the smallest possible value that can be stored using a 4-bit exponent would be represented by decimal -7 which is binary 0000

There's not really any method to answering that question though - it's just a matter of whether or not you understand that the exponent is negative-biased.

However, you're right that the mantissa would be binary 00000001 which is a decimal value of 2^(-8).

(and together, those would give you a decimal value of 2^(-8) * 2^(-7) which of course is equal to 2^(-15).)

Can you explain how 0000 is - 7 please?