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A quiz for the ee 2030 course at the georgia institute of technology. The quiz covers topics such as binary number conversion, logic gates, and digital circuits. Students are required to answer problems related to adding binary numbers in 2's complement form, implementing logic functions using nand gates, and designing state machines for digital communication systems.
Typology: Exams
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Problem 1 (20 pts):
a. (8 pts) Convert the following numbers (all binary numbers are in 2’s complement form):
01101.101 binary =⇒ decimal
-13 decimal =⇒ binary (8 bit)
11010011 binary =⇒ decimal
1010.0101 binary =⇒ decimal
01010101 binary =⇒ decimal
17 decimal =⇒ binary (8 bit)
-2 decimal =⇒ binary (8 bit)
b. (4 pts) Add the following unsigned, 5 bit, binary numbers; indicate if there has been an overflow error:
1010
overflow? overflow? overflow? overflow?
c. (8 pts) Add the following 5 bit, 2’s complement binary numbers, indicate if there has been an overflow error:
1010
overflow? overflow? overflow?
overflow? overflow? overflow?
Problem 3 (20 pts):
a. (10 pts) Often, in digital communications, a code is sent to mark the beginning of a mes- sage. The state diagram shown below detects the sequence 11010 with overlapping codes not permitted. For this state machine there is one input, the digital signal x, and one output, the detect signal D. Fill in the state table below based on the state diagram.
000/
001/0 010/
011/
101/1 100/
0
0
1
0
1
1
0
1
0
1
Current State Input Next State Output S 2 S 1 S 0 x N S 2 N S 1 N S 0 D 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 1 0 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1
b. (10 pts) Suppose we want to make an timer which counts down from 5 to 0. When the timer reaches 0 a bell rings and continues to ring until the OK button is pressed. When the OK button is pressed the timer starts over at 5 again. The OK button causes the OK input to go high. Draw a state diagram for a Moore type state machine that will implement the timer as described. Label the diagram clearly.
Problem 5 (24 pts):
a. (8 pts) The bottom segment of a numeric LED display is only lit when the numbers 1, 4, 7, and 9 are displayed. Assume that the number to be displayed is determined by the binary number represented by the four input lines A 3 − A 0. Also assume that we do not care what is displayed if the input value is greater than 9. Fill in the truth table for the bottom LED driver (F 0 ).
A 3 A 2 A 1 A 0 F 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 1 0 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1
b. (4 pts) From your truth table, fill in the K-map for simplifying the expression for F 0. You do not need to simplify the expression, just fill in the table.
@ @@
00
}
}
︷ ︸︸ ︷︷ ︸︸ ︷
︸ ︷︷ ︸︸ ︷︷ ︸︸ ︷︷ ︸
c. (6 pts) The K-map corresponding to the top LED driver (F 6 ) is shown below. Write down the simplified expression for F 6.
@ @@
00
}
}
︷ ︸︸ ︷︷ ︸︸ ︷
︸ ︷︷ ︸︸ ︷︷ ︸︸ ︷︷ ︸
1 1 x x
x x x x
d. (6 pts) Implement F 6 using your choice of gates, multiplexers, or decoders.
