Department of Electrical and Computer Engineering McGill University ...
Department of Electrical and Computer Engineering McGill University ECSE-221 Introduction to Computer Engineering I Mid Term Exam Examiner: F.P. Ferrie Question 1
Date: February 14th, 2003
(2 points)
A computer uses a 14-bit word for representing signed integers. If the scheme chosen is 2’s complement, then what is the range of numbers represented? Question 2
(2 points)
Two 8-bit unsigned integers are multiplied using the algorithm in Assignment 1. If the multiplicand and multiplier are 57 and 71 respectively, then what is the value of the partial product (i.e. sum) at the end of the second iteration? Question 3
(4 points)
Encode the number 9.67 x 1014 using IEEE 754 single precision representation. Express your answer in hexadecimal form. (Compute mantissa to equivalent precision of input.) Question 4
(2 points)
A signal with range [-5v,5v] must be sampled with a resolution of 1.0 mV. How many digits would be required to represent this number if a base-5 system were used? Question 5
(2 points)
What is produced by the following snippet of “C” code? int main (int argc, char *argv[]) { char a = 'A'; printf("The output is %c.\n",(a|0x20)+1); }
Question 6
(6 points)
Determine the minimal ∑∏ and ∏∑ forms for the function f(A,B,C,D) with maxterms (1,3,4,6,9,11,12,14) = 0. Maxterms 7 and 13 are don’t care. Prove algebraically that both forms are equal if the don’t care terms are both equal to 1. Question 7
(2 points)
Draw the NAND-NAND and NOR-NOR implementations for the minimal forms in Question 6. Question 8
(2 points)
Draw the circuit diagram for a 4-input multiplexer such that Tpd from any data input = 2Tg. (turn over – more questions on back)
Question 9
(2 points)
Analyze the logic gate shown below. Determine its function, F, and corresponding gate delay, Tg, assuming that the switching elements require 500nS to turn on and 750ns to turn off. +5V
X Y F
Question 10 (2 points) Determine the number of distinct 3 input binary functions that are possible. Question 11 (4 points) Write down the state transition table corresponding to the circuit shown below and determine its response to the inputs given in the accompanying timing diagram. (You may fill in the response on the exam question sheet, or reproduce the timing diagram in your answer booklets).
S
C
R
Timing diagram
Q
Date: February 14th, 2003
(2 points)
A computer uses a 14-bit word for representing signed integers. If the scheme chosen is 2’s complement, then what is the range of numbers represented? Question 2
(2 points)
Two 8-bit unsigned integers are multiplied using the algorithm in Assignment 1. If the multiplicand and multiplier are 57 and 71 respectively, then what is the value of the partial product (i.e. sum) at the end of the second iteration? Question 3
(4 points)
Encode the number 9.67 x 1014 using IEEE 754 single precision representation. Express your answer in hexadecimal form. (Compute mantissa to equivalent precision of input.) Question 4
(2 points)
A signal with range [-5v,5v] must be sampled with a resolution of 1.0 mV. How many digits would be required to represent this number if a base-5 system were used? Question 5
(2 points)
What is produced by the following snippet of “C” code? int main (int argc, char *argv[]) { char a = 'A'; printf("The output is %c.\n",(a|0x20)+1); }
Question 6
(6 points)
Determine the minimal ∑∏ and ∏∑ forms for the function f(A,B,C,D) with maxterms (1,3,4,6,9,11,12,14) = 0. Maxterms 7 and 13 are don’t care. Prove algebraically that both forms are equal if the don’t care terms are both equal to 1. Question 7
(2 points)
Draw the NAND-NAND and NOR-NOR implementations for the minimal forms in Question 6. Question 8
(2 points)
Draw the circuit diagram for a 4-input multiplexer such that Tpd from any data input = 2Tg. (turn over – more questions on back)
Question 9
(2 points)
Analyze the logic gate shown below. Determine its function, F, and corresponding gate delay, Tg, assuming that the switching elements require 500nS to turn on and 750ns to turn off. +5V
X Y F
Question 10 (2 points) Determine the number of distinct 3 input binary functions that are possible. Question 11 (4 points) Write down the state transition table corresponding to the circuit shown below and determine its response to the inputs given in the accompanying timing diagram. (You may fill in the response on the exam question sheet, or reproduce the timing diagram in your answer booklets).
S
C
R
Timing diagram
Q
