# Final exam for CSCI 274

This is an open book, open notes exam; however, the use of
calculators is forbidden. The exam is to be turned in by 8:30
PM.

## Problem 1. (10 points)

Convert the following decimal numbers into 10-bit
two's-complement binary numbers

## Problem 2. (10 points)

Represent the following 10-bit two's-complement numbers as
decimal numbers

## Problem 3. (10 points)

Convert the decimal number 6.65 into a floating point number
with one sign bit, an eight-bit exponent expressed using excess-127
notation, and a 23-bit mantissa. By the way, if it takes you a long
time to derive the mantissa, you are doing something wrong.

## Problem 4. (10 points)

Use *either* a truth table *or* Boolean algebra to
show that the following two Boolean expressions are equivalent:

`A` ( `A` + `B`' `C` +
`A`' ) + `B`
`A` + `B`

## Problem 5. (10 points)

Draw a sum-of-products circuit implementation of the following
Boolean expression

## Problem 6. (10 points)

Now implement the Boolean expression, ( `x` +
`y` ) `z`', of the previous problem using only
four two-input NAND gates. Hint: Start with the sum-of-products
implementation.

## Problem 7. (10 points)

If registers `A` and `B` have the following
values:

`A` = 0011001010
`B` = 1000101110

what are the values of the following five expressions

`A` + `B` |
+ is ordinary addition |

`A` - `B` |
- is ordinary addition |

`A` *AND* `B` |
*AND* is bit-wise logical and,
C's `&` operator, the upside-down V |

*asl* `B` |
*asl* is arithmetic shift left |

*csl* `B` |
*csl* is circular shift left |

## Problem 8. (10 points)

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

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

what happens in the next bus transaction?

## Problem 9. (10 points)

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?

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

## Problem 10. (10 points)

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

What action is performed when these five words are executed in order?