Convert the decimal number 89 into a binary number.

Convert the binary number 110110011 into a decimal number.

Represent the decimal number -100 as a twelve-bit two's complement binary number .

Convert the decimal number 14.62 into a floating point number with one sign bit, an eight-bit exponent expressed using excess-127 notation, and a 23-bit mantissa.

Use truth tables to show that the following two Boolean expressions are equivalent:

*A*(*A**C*+*A*'*C*) (*B*+*C*)*A**C*

Now, simplify the following Boolean expression, from the previous problem, using Boolean algebra. It is very important to show your work!

*A*(*A**C*+*A*'*C*) (*B*+*C*)

Simplify the following Boolean function using a Karnaugh map. Notice the don't care conditions!

- F(
*a*,*b*,*c*,*d*) = Sigma(1, 4, 7, 9, 10, 14) - F(
*a*,*b*,*c*,*d*) = d(3, 8, 11, 13, 15)

How many different values can be stored in an eight-bit register.

Draw the symbol used in diglog to represent an input pad, the thing your mashed to generate a zero or one, in the space below.

If registers `S` and `T` have the following
values:

`S`= 0011110011`T`= 1111100000

what are their values after each of the following RTL statements are performed

`S`<-`S`and`T`,`T`<-`S`-`T``T`<-*asl*`S`

where *asl* is the arithmetic shift left operator.

Show the hardware needed to implement the following RTL
statements for eight-bit registers `A` and `B`:

*p*:`A`<-`A`+1,`B`<-`A`*q**r*:`A`<-`A`-1

You may use eight-bit adders, eight-bit multiplexers, eight-bit registers, and assorted logic gates in your solution.

Look at Figure 5-4 on page 130 of the textbook, if

`S2 S1 S0`= 001- LD of
`IR`is set - LD of
`PC`is set - INR of
`DR`is set

what happens in the next bus transaction?

How would you set the control inputs of the bus system shown in Figure 5-4 on page 130 of the textbook to execute the following RTL statement?

`M[AR]`<-`DR`,`DR`<- 0

Suppose the following 16 bits hexadecimal values is stored in the memory of the "basic computer" described in Table 5-2 on page 133 of the textbook.

`A200`

What action is performed when this word in executed as an instruction?

Do you think there are more microcode programmers than assembly language programmers? Justify your answer.

Write a procedure in the textbook's assembly language, using the calling conventions described in Section 6-7 (pp. 200-202), equivalent to the following C subroutine

int useless(int a) { if (a & 1) return(a) ; else return(a+1) ; }

Hint for the non-C experts: This function returns `a`, if
`a` is odd, and `a+1`, if `a` is even.

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