(Solved): 11. Convert between binary and decimal representations: (a) 11.475 to binary (b) Binary 1100000110 ...

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) $$\mathrm{B}2{\mathrm{U}}_5(0\times 2\mathrm{E})$$ (b) $${\mathrm{B}}_2{\mathrm{T}}_5(0\times 2\mathrm{E})$$ 7. Apply the function $$T2U_5$$ 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) $$?127==127\mathrm{U}$$ (b) $$?127?1U==127$$ (c) $$?1\mathrm{U}<128\mathrm{U}$$ (d) $$255\mathrm{U}==?128$$ 9. Express $$x^{?}K$$ using on only the specified number of operations: (a) $$\mathrm{K}=7$$, using 1 shift and $$1\mathrm{Add}/$$ Sub (b) $$K=?13$$, using the fewest possible shifts and Add/Subs 10. Write $$\mathrm{C}$$ expressions that evaluate to 1 when the following conditions are true and to 0 when they are false. Assume $$x$$ is of type int. (a) Any bit of $$x$$ equals 1 . (b) Any bit of $$x$$ equals 0 . (c) Any bit in the least significant byte of $$x$$ equal