Submit your solutions by Friday, February 15, 2019 10am. Remember, when appropriate, to justify your answers.

1. [5 marks] Floating-Point Conversion

(a) [3 marks] Convert -255, -2.55 and 1/3 into the equivalent 32-bit floating-point. In all cases, show

your steps and express your final answer both in binary and hex.

(b) [2 marks] Convert the 32-bit floating-point 0x3e970a3d and 0x3f7fffff into their numerical equivalents. Express each as normalized base-2 scientific notation, as a base-10 rational fraction, and as a base-10 decimal value. Round your answers to 10 decimals. For example, if you were to convert 0x3f200000, the expected answers would be: 1.01 21, 5 , and 0.6250000000.

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2. [6 marks] Half-Precision Floating-Point

Suppose there was a floating-point code that fit in 16 bits, with 1 bit for the sign, 4 bits for the exponent

and 11 bits for the significand.

sign exponent significand

Answer the following questions. Be sure to justify your answers.

(a) [1 mark] What is the range of normalized exponents?

(b) [1 mark] Excluding +, and NaN, how many different values can be encoded?

(c) [1 mark] What is the median value of the code?

(d) [1 mark] What is the range of positive denormalized values?

(e) [1 mark] What is the range of positive normalized values?

(f) [1 mark] What is the median of the positive normalized values?

(g) [1 BONUS mark] What is the median of the positive values?

CMPT 295 Assignment 4 (2%) Submit your solutions by Friday, February 15, 2019 10am Remember, when appropriate, to justify your answers. 1. 15 marks) Floating-Point Conversion (a) 3 marks] Convert-255, -2.55 and 1/3 into the equivalent 32-bit floating-point. In all cases, show your steps and express your final answer both in binary and hex (b) 2 marks Convert the 32-bit foating-point 0x3e970a3d and Ox37 into their mmerical equivalents. Express each as ormalized base-2 scientific notation, as a base-10 rational fraction and as a base-10 decimal value. Round your answers to 10 decimals. For example, if you were to convert Ox31200000, the expected answers would be: 1.01 x 2-, and 0.6250000000. 2. 6 marks] Half-Precision Floating-Point Suppose there was a floating-point code that fit in 16 bits, with 1 bit for the sign, 4 bits for the exponent and 11 bits for the significand. sign exponent significanod Answer the following questions. Be sure to justify your answers (a) markl What is the range of normalized exponents? (b) I mark) Excluding too,-oo and NaN, how many different values can be encoded? c)1 mark] What is the median value of the code? (d) mark What is the range of positive denormalized values? e) mark What is the range of positive normalized values? (f) [I markl What is the median of the positive normalized values? () BONUS mark] What is the median of the positive values