Question

3.8) Convert the hexadecimal number 0x15 to a decimal number.

3.9) Convert the hexadecimal number 0x19 to a decimal number.

3.10) Convert the decimal number -35 to an 8-bit two’s complement binary number.

3.11) Convert the decimal number -32 to an 8-bit two’s complement binary number.

3.12) Assuming the use of the two’s complement number system find the equivalent decimal values for the following 8-bit binary numbers:

a)10000001

b)11111111

c)01010000

d)11100000

e)10000011

3.13) Convert the base 8 number 204 to a decimal number.

3.14) Convert the base 7 number 204 to a decimal number.

3.15) Convert the base 6 number 204 to a decimal number.

3.16) Convert the base 5 number 204 to a decimal number.

3.17) Convert the base 10 number 81 to a base 9 number.

3.18) For each row of the following table, convert the given number to each of the other two bases, assuming the two’s complement number system is used:

16-Bit Binary Hexadecimal Decimal

1111111100111100

0xFF88

128

1111111111111010

0x0011

-25

3.19) You are given the following two numbers in two’s complement representation:

01101110

00011010

Perform the binary addition. Did signed overflow occur? Explain how you determined whether or not overflow occurred.

3.20) In this chapter, the one’s complement number system was never mentioned, but at http://courses.cs.vt.edu/csonline/NumberSystems/Lessons/ you can learn about it. Explain the major trade-offs between using the one’s or two’s complement system.

3.21) You are given the following two numbers in two’s complement representation:

11101000

-00010011

Perform the binary subtraction. Did signed overflow occur? Explain how you determined whether or not overflow occurred.

3.22) Sign extend the two-digit hex number 0x88 to a four-digit hex number. 0x .

3.23) The following subtract instruction is located at address 0x00012344:

Loop: addi $t4, $t4, -8

sub $t2, $t2, $t0

bne $t4, $t2,loop

What are the two possible values for the contents of the PC register after the branch instruction has executed? 0x . 0x .

This branch instruction is described in Appendix C.

3.24) You are given the following two 8-bit binary numbers in the two’s complement number system:

X = 100101002 = 10 Y = 001011002 = 10

What values do these numbers represent in decimal? Perform the following arithmetic operations on X and Y:

X + Y X-Y Y-X

10010100 10010100 00101100

00101100

Show your answers as 8-bit binary numbers in the two’s complement number system. To subtract Y from X, find the two’s complement of Y and add it to X. Indicate whether overflow occurs in performing any of these operations.

Now show a solution to the same arithmetic problems using the hexadecimal representations of X and Y.

3.25) The following code segment is stored in memory starting at memory location 0x00012344:

loop: lw $t0, 0($a0) #

addi $a0, $a0, 4 #

andi $t1, $t0, 1 #

beqz $t0, loop #

What are the two possible values for the contents of the PC after the branch instruction has executed? In the comments field, add a pseudocode description for each instruction.

0x . 0x .

Answer 1

3.8) decimal number is "21"

3.9) decimal number is "25"

3.10) 11011101

3.11) 11100000

3.12)

     a) -127

     b) -1

     c) 80

     d) -32

     e) -125

3.13) 132

3.14) 102

3.15) 76

3.16) 54

3.17) 100

3.18)

3.19) 10001000

3.21)

3.22)

3.23)

3.24)x=

3.25)