CEG2136/CEG2536 Computer Architecture I Architecture des ordinateurs I MIDTERM EXAMINATION

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Java Python CEG2136/CEG2536 Computer Architecture I

Architecture des ordinateurs I

MIDTERM

EXAMINATION

Instructions:

. Answer ALL questions on the questionnaire.

. This is a close-book examination.

. Use the provided space to answer the following questions. For your calculations you can use pages 6-8.

. Calculators are not allowed.

. Read all the questions before you start.

Q1. The range of signed integers N expressed in 2-s complement representation that can be

stored in a 10-bit register is:

(a) -1024≤N≤+1023 (b) -1023≤N≤+1024 (c) -512≤N≤+511 (d) -511≤N≤+512

(e) None of the above

Q2. Identify the decimal number which is represented next in floating point with the IEEE

754 standard: 11000010100010101100000000000000

(a) (- 133.375)10 (b) (- 69.375)10 (c) (- 138.750)10 (d) (- 34.6875)10 (e) (- 8.671875)10

Q3) Give the best binary approximation of A = (26.6)10 and B = - (23.4)10 employing signed

2’s-complement representation with 2 bits for the fractional part. A = B =

Q4) 1) Convert to decimal the following two numbers, 01010 & 10101, which are already

expressed in 2’s complement representation.

2) These numbers are stored in two 6-bit registers X and Y to calculate their sum

(S = X+Y) and their difference (D=X-Y) by using additions and 2’s complementation only. Convert to decimal and write each intermediate and final result, to check the correctness of

your assertions.

S = X+Y 2’s complement Base 10 D=X-Y 2’s complement Base 10

CY: X + Y

CY: X + -Y D

3) Since both S and D have to be represented with 6 bits, indicate if overflow occurs, and explain how a circuit can detect these situations.

Q5. Which of the logic functions is implemented by the following circuit?

A' B'

C D

(a) f(A,B,C,D) = Σm(4,5,6,7,8,9,10)+X(12,13,14,15) (b) f(A,B,C,D) = Σm(4,5,6,8,9,10,14)

(d) f(A,B,C,D) = Σm(0,1,2,3,7,11,15)

(e) f(A,B,C,D) = Σm(4,5,6,8,9,10,12,13,14)+X(7,11)

Q6. Which of the following logic functions is implemented by the given circuit?

MUX 8x1 (1 bit)

0 1 2 3 4 5 6 7

D 0 0 D, D 1 D, 1 (e) f(A,B,C,D) = Σm(1,6,9,10,11,12,14,15)

Q7. What is the capacity of a ROM, capable to implement three functions of six variables?

(a) 8 words of 6 bits (b) 16 words of 3 bits (c) 32 words of 6 bits (d) 64 words of 3 bits

(e) None of the above

Draw a block diagram of your memory with the major components, indicating its inputs and outputs.

Q8.

1) - Draw the state diagram of the sequential circuit whose state table is given below

Present Next The State Diagram goes here:

State state

CEG2136/CEG2536 Computer Architecture I Architecture des ordinateurs I MIDTERM EXAMINATION

A B C	A+B+C+	JA	KA	JB	KB	JC	KC
0 0 0	1 0 0
0 0 1	1 1 0
0 1 0	0 0 1
1 0 0	0 1 0
1 1 0	0 0 0

- Fill out the above table with the appropriate values for the JK flip-flops inputs such that the sequential circuit will observe the required transitions.

- Indicate the correct set of minimized equations of the JK flip-flops inputs from the following:

(a) J A = A,B,, (b) J A = A,B,, (c) J A = B,,

(d) J A = A,B,, (e) J A = B,,

KA = C,, KA = 1, KA = 1, KA = A, KA = A,

JB = AB’C’+ A’B’C,

JB = A+C, JB = A+C, JB = AC, JB = AC,

KB = BC,, KB = 1,

KB = 1, KB = C,, KB = C,,

JC = A’BC JC = A,B, JC = A,B, JC = A,BC, JC = A,BC,

KC = A’B’C. KC = 1.

KC = 1. KC = A,. KC = A,.

2) - If your circuit reaches by mistake any of the 3 states that are not used, determine their corresponding next state.

Present state	Next State

- Is your circuit auto-corrective? Reply just with YES or NO

Draw the time diagram and give the states of the flip-flops’ outputs through the first 6 clock pulses, assuming that their initial state (at t=0) is 000 and they are triggered on the rising edge of the clock