Consider the two floating point systems defined below. They are similar to the one presented in the lecture, however, have different lengths for mantissa and exponent.

Both have 13 bit length in total. Their structure is as follows:

System 1: 1 sign bit, 8 exponent bits (excess 128 system), 4 mantissa bits (non-normalized form)

System 2: 1 sign bit, 4 exponent bits (excess 8 system), 8 mantissa bits (non-normalized form)

Hint: The sign bit is 0 for positive numbers, the exponent is encoded in the excess system which has a sign bit 1 for positive numbers.

In which of the systems is the number 1 0001 0000 1000₂ (spaces for ease of reading, only) larger than in the other system (please consider the sign)?

System 1

System 2

Same in both

Give reason to your answer (required!):

What is the next larger number with the smallest difference to 1 0001 0000 1000₂ in System 1 (in above binary floating point code)? Consider the sign!

Give reason to your answer (required!):

What is the next largest number with the identical mantissa to 1 0001 0000 1000₂ in System 1 (in above binary floating point code)? Consider the sign!

Give reason to your answer (required!):