The floating-point format to be used in this problem is an 8-bit IEEE 754 normalized format with 1 sign bit, 4 exponent bits, and 3 mantissa bits. It is identical to the 32-bit and 64-bit formats in terms of the meaning of fields and special encodings. The exponent field employs an excess- 7coding. The bit fields in a number are (sign, exponent, mantissa). Assume that we use unbiased rounding to the nearest even specified in the IEEE floating point standard.

(a) Encode the following numbers the 8-bit IEEE format: (1) 0.0011011binary (2) 16.0decimal

(b) Perform the computation 1.011binary + 0.0011011binary showing the correct state of the guard, round and sticky bits. There are three mantissa bits.

(c) Decode the following 8-bit IEEE number into their decimal value: 1 1010 101

(d) Decide which number in the following pairs are greater in value (the numbers are in 8-bit IEEE 754 format): (1) 0 0100 100 and 0 0100 111 (2) 0 1100 100 and 1 1100 101

(e) In the 32-bit IEEE format, what is the encoding for negative zero? (f) In the 32-bit IEEE format, what is the encoding for positive infinity?