ELEC2141 – DIGITAL CIRCUIT DESIGN MID-SEMESTER EXAMINATION SESSION 1, 2018
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ELEC2141 – DIGITAL CIRCUIT DESIGN
MID-SEMESTER EXAMINATION
SESSION 1, 2018
Question 1 (50 marks)
a) Consider the following Boolean function F:
(
, 
, 
, 
) = (
̅ + 
)(
̅ + 
)(
+ 
) + (
+ 
)(
+ 
̅ + 
)
Assuming that the function F is implemented using basic logic gates (NOT, AND and OR gates),
i. Find the total gate input-cost of the implementation. [5 marks]
ii. Express the function F as a sum-of-minterms (you may use the “little m” short cut notation). [7 marks]
iii. Simplify the function F using a Karnaugh map and express it as the sum-of-products. List all prime implicants and essential prime implicants. [15 marks]
iv. For your design in part (iii), find the reduction in the total gate-input cost as compared to part (i). [3 marks]
b) Convert the numbers in the table below from the given base to the other three bases. limit the number of digits in the fraction part to six for the binary form. Show all your workings. [10 marks]
|
binary |
decimal |
hexadecimal |
octal |
|
|
|
2B.5 |
|
c) What is a priority encoder circuit, and how does it differ from a regular encoder? Draw a block diagram of a 4-to-2 priority encoder. On the block diagram, labels the possible inputs applied to the encoder if only the most significant output bit is equal to 1. [10 marks]
Question 2 (50 marks)
a) Consider the following Boolean function F:
(
, 
, 
, 
) = 
̅ + 
̅
+ 
+ 
̅
Assuming that the function F is implemented using basic logic gates (NOT, AND and OR gates),
i. Using Boolean algebraic manipulation, show that 
= 
̅
+ 
̅ + 
. [10 marks]
ii. Using the principle of duality, convert F to POS form. [5 marks]
iii. Draw the logic circuit using NAND only gates assuming no complemented signals are available. [10 marks]
b) Design a digital system with the following characteristics and criteria. There are four inputs (A, B, C, D) and one output (Y) to the system. The output Y is true (i.e. logic “1”) when ABCD is greater than 7 and the binary input value is odd. When the binary value of ABCD is less than or equal to 7, output Y follows the result of the expression B ⊕ C. You can assume A is the most significant digit and D is the least significant digit.
i. Draw the truth table for the four inputs (A, B, C, D) and one output (Y). [10 marks]
ii. Express the function F as a sum-of-minterms (you may use the “little m” short cut notation). [5 marks]
iii. Implement the following Boolean function with a 4x1 multiplexer and the minimum number of 2-input external gates and inverters only. Do not assume that complements are available. [10 marks]
2022-03-10