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ECE 2030K
Dr. Robert Butera
Final Exam
December 15, 1999
- This is an open-book open-notes exam. You can use any printed non-electronic refer- ence material. NO CALCULATORS, COMPUTERS, PDAS, ETC.
- You may ask me to clear up anything vague about a particular question.
- YOU MAY NOT ask anyone else in the class for assistance, or offer assistance of any kind to a classmate.
- You are bound by the Academic Honor Code as set forth on pages 336-339 of the Georgia Tech 1999-2001 General Catalog.
- Show your work - it is a lot easier to give partial credit when I know how you got the answer you did. Neatness and readability helps, too. I have provided a lot of space with each problem as well as extra pages in case you need them.
- It is a good idea to look over the entire test, and how many points each problem and subproblem are worth, before proceeding. It is also a good idea to look over an entire question before answering it, since there may be subsequent parts to that question on the following page.
Problem # Points Score
TOTAL 100
Name
Student
- 10 points Boolean Algebra. The next page is blank if you need it.
(a) 4 points Using basic boolean algebra identities, simplify the following into a sum- of-products:
F = (A + BC)D
For the remaining parts of this question,
G(A, B, C) =
∑ m(0, 1 , 5 , 7)
(b) 2 points Express G as a sum-of-products using minterms. You do not have to simplify anything. Circle your answer.
(c) 2 points Express G as a product-of-sums using maxterms. You do not have to simplify anything. Circle your answer.
(d) 2 points Express G as a sum-of-products using minterms. You do not have to simplify anything. Circle your answer.
- 30 points Combinatorial Logic.
(a) 6 points Implement the following function using switch-logic. You do not have inverted inputs available.
F = ABC
The remaining questions refer to the following function:
G = (AB + CD)E + EF
(b) 4 points Using mixed-logic notation (AND/OR gates with vertical bars to indicate
inversion), draw an idealized circuit that implements the exact function as written above.
For parts (c) and (d), you may want to use the blank page that follows this one. (c) 4 points If the above circuit is implemented with just NAND gates and INVERT- ERS, how many transistors are required?
(d) 4 points If the above circuit is implemented with just NOR gates and INVERT- ERS, how many transistors are required?
(e) 6 points Using the K-map below, circle ALL the prime implicants. Write the simplified equation on the line, and circle all the terms in the equation that are essential prime implicants.
F (A, B, C, X) =
AB
A
B
CX X
C
(f) 6 points Using the K-map below with don’t care conditions, write the simplified equation on the line below. Be sure the corresponding terms are circled in the K-map.
G(A, B, C, X) =
AB
A
B
CX X
C
X X
X
X
- 23 points Fun with State Machines. Consider the state machine below. It has one
input (E), one output (T ), and 2 state variables (A,B). The J-K and D flip flops are edge-triggered.
J
K
Q
Q
CLK
CLK
Q
Q
D
A
A
B
B
E
S
S
S
D D D D D D D D
3:8 DECODER
T
(a) 8 points Fill in the state-transistion table below. Filling in JA, KA, and DB is optional.
present input next output A B E JA KA DB A B T 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1
- 10 points Memory system design. You need to design a 2Mb X 32 memory system for a new computer. You only have 256Kb X 16 DRAM memory chips available. (a) 2 points How many DRAM chips do you need?
(b) 2 points How many address lines are required as input to your memory system?
(c) 2 points How many address lines are available per chip?
(d) 2 points How many data lines are available per chip?
(e) 2 points What type of decoder will be necessary to select the right memory chip(s)?
Extra space for work
- 27 points Datapath/Architecture/Instruction Sets.
.data cat: .word 0x249A2DC
.align 2 .globl main
.text main: lw $t0,cat($0) li $t1, li $t2,0xF move $t3,$ li $t7, dog: and $t4,$t0,$t add $t3,$t3,$t srl $t0,$t0,$t addi $t1,$t1,- bne $t1,$0,dog
done: li $v0, syscall
The first few questions concern the above program. The questions concern the purpose or role of each register, so please do not provide a simple answer like “register A is added to register B” (a) 4 points By the time the program reaches the label done, what is the contents (in hex) of register $t3?
(b) 3 points In the above program, what is $t2 used for?
(c) 3 points In the above program, what is $t4 used for?
(d) 2 points In the above program, what is $t3 use for?
