11. Convert between binary and decimal representations: (a) 11.475 to binary (b) Binary 110000011001111 to hexadecimal (c) Binary 101.1111 to decimal 12. Show the result of rounding to the nearest 1/8 according to the round-to-even rule: (a) 11.0001 (b) 11.0010 13. We have a 9bit FP representation based on the IEEE 754 standard: 1 for the sign, 4 for the exponent and 4 for the fraction. You may need to round. You should show your work for partial credit. Please show answers in binary. (a) Represent 0.125(1/8) in this system. (b) Represent 5.25 in this system. (c)Obtain the product of the two numbers from (a) and (b) above: - Add the two exponents using exponent encoding: - Multiply the two significands including rounding: - Give the result in 9-bit binary format. (d)Obtain the sum: - Normalize so both have same exponent: - Now show the sum, which may require normalizing exp or rounding. 14. What decimal value is represented by the following bit string when interpreted as a single precision floating point value: 0x43008000? 15. Represent decimal 63.0 as a single precision floating point value (in hex). 6. Write out and sum the non-zero powers of two for the two functions shown. Express output in decimal: (a) B2U5(02E) (b) B2T5(02E) 7. Apply the function T2U5 to the two following decimal values. Express the answer as a decimal number. (a) 7 (b) 12 8. Assuming an 8-bit machine that uses 2 's complement arithmetic, apply the appropriate casting and express the result as a relational value (true or false): (a) 127==127U (b) 1271U==127 (c) 1U