## Description

1. [20] Suppose we number the bits in a 32-bit word from 0 (least significant) to 31 (most

significant). Write code for the following C function that will return a bit mask containing 1s for

the least-significant n bits and 0s for the remaining most-significant bits:

int mask(int n);

Your solution will need to handle the case that mask is called with input 32 (hint: shifting a 32-

bit word by 32 in either direction is undefined in standard C, so don’t do it; another hint: the int

return type can be exploited to handle this case).

Here are some test runs:

mask(1): 0x1

mask(2): 0x3

mask(3): 0x7

mask(5): 0x1F

mask(8): 0xFF

mask(16): 0xFFFF

mask(32): 0xFFFFFFFF

Use only bitwise operators and subtraction; no if statements, loops, or other arithmetic

operators (+, *, /, %). Also write a main() function to test your function. Name your source file

2-1.c

2. [20] Suppose we number the bytes in a 32-bit word from 0 (least significant) to 3 (most

significant) and that the word consists of 4 individual signed bytes. Write code for the following

C function that will return byte i of x sign extended to 32 bits:

unsigned int extract (unsigned int x, int i);

Here are some test runs:

extract(0x12345678, 0): 0x00000078

extract(0xABCDEF00, 2): 0xFFFFFFCD

Use only bitwise operators and subtraction; no if statements, loops, or other arithmetic

operators (+, *, /, %). Also write a main() function to test your function. Name your source file

2-2.c

3. [15] Fill in the missing expression in the following C code such that it will return 1 if x is >= y,

0 otherwise (you can assume that neither argument is NaN and that +0 and -0 are considered

equal):

int ge(float x, float y) {

unsigned ux = *((unsigned *) &x); // convert x raw bits

unsigned uy = *((unsigned *) &y); // convert y raw bits

unsigned sx = ux >> 31; // extract sign bit of ux

unsigned sy = uy >> 31; // extract sign bit of uy

ux <<= 1; // drop sign bit of ux
uy <<= 1; // drop sign bit of uy
// TODO: return using sx, sy, ux, uy
}
Here are some test runs:
ge(0.0f, 0.0f): 1
ge(-0.0f, 0.0f): 1
ge(-1.0f, 0.0f): 0
ge(0.0f, 1.0f): 0
ge(1.0f, 0.0f): 1
ge(0.0f, -1.0f): 1
Use only bitwise operators; no if statements, loops, or arithmetic operators (+, -, *, /, %). Also
write a main() function to test your function. Name your source file 2-3.c
4. [15] Convert the following hex values to decimal assuming that they are stored as 2s
complement integers.
a. (5) 0x000000FF
b. (5) 0xFFFFFCE6
c. (5) 0xFFFFFFFF
Write your answers in your solutions document. Show your work.
5. [15] Convert the following hex values to decimal assuming that they are encoded as IEEE 754
single-precision floating-point numbers:
a. (5) 0x80000000
b. (5) 0x41220000
c. (5) 0xC39D0000
Write your answers in your solutions document. Show your work.
6. [15] Convert the following decimal numbers to hex encoded as IEEE 754 single-precision
floating-point numbers. Write your answers in your solutions document.
a. (5) 1.0
b. (5) 8.25
c. (5) -25.125
Write your answers in your solutions document. Show your work.
Zip the source files and solution document (if applicable), name the .zip file

Assignments section for submission link).