Computer Science Homework Help

Long Assignment 3

Computer Architecture — CDA3102

Knight Foundation School of Computing & Information Sciences Florida International University

1. (40 points) Let a = 0XD3 and b = 0XA9.
   1. (a) (15 points) Assuming that a and b are two unsigned integers, find a + b, a − b, a ×b, a/b, and a%b. Represent the result using unsigned 16-bit representation.
   2. (b) (15 points) Assuming that a and a are two two’s complement 8-bit signed integers, find a + b, a − b, a × b, a/b, and a%b. Represent the result using two’s complement 16-bit representation.
   3. (c) (5 points) Write-down the results of parts a and b in Hexadecimal base.
   4. (d) (5 points) Write-down the results of parts a and b in Octal base.
2. (10 points) Let 0XF0F0F0F0 represent a floating-point number using IEEE 754 single precision notation. Find the numerical value of the number. Show the intermediate steps.√
3. (15 points) Let α = 2.

(a) (5 points) Find the binary scientific notation of α with five bits after the binary

point; i.e. find integer n and bits x1, x2, . . . , x5 such that α = 1.x1x2x3x4x5 × 2n.

√

2. (Hint: First, 247 using a scientific calculator that supports long numbers with 15 decimal digits. Then, round the result to the closest integer like m. Finally, find the

(b) (10 points) Find the single-precision IEEE 754 representation of

find

√

floating point representation of √2 = m/223) 4. (35 points) Let a = 37.3125 and b = 1.6125.

1. (a) (10 points) Find the double-precision IEEE 754 representation of a and b in hex- adecimal base.
2. (b) (5 points) Find the single-precision IEEE 754 representation of a and b in hex- adecimal base.
3. (c) (10 points) Find the single-precision IEEE 754 representation of a + b in hexadec- imal base.
4. (d) (10 points) Find the single-precision IEEE 754 representation of a × b in hexadec- imal base.

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