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EE 2301 Introduction to Digital Systems Design Fall 2024 Homework 2

Due Wed., Oct. 16, 2024, at 11:59pm

No late homeworks will be accepted.EE 2301, Fall ’24

1. Consider a circuit that accepts as inputs four bits x2, x1, x0. These specify which of the digits in your 7-digit student ID to choose. Consider a circuit with four outputs y3, y2, y1, y0 that produce the corresponding digit.

For instance, suppose that your student ID is 3451234. Given an input of 101 for x2, x1, x0, the circuit should produce the fifth digit (starting at zero) so “4” in the example above, so 0100 for y3, y2, y1, y0.

Truth Table Design

Fill in the following truth table. Include “don’t care” outputs when appropriate.

inputs			outputs
x2	x1	x0	y3	y2	y1	y0
0	0	0
0	0	1
0	1	1
1	0	0
1	0	1
1	1	0
1	1	1

• Write a minimal AND-OR (i.e., sum of products) two-level expression for this function.

• Write a minimal NAND-NAND two-level expression for this function.

• Write a minimal OR-NAND two-level expression for this function.

• Write a minimal NOR-OR two-level expression for this function.

• Write a minimal OR-AND (i.e., product-of-sums) two-level expression for this function.

• Write a minimal NOR-NOR two-level expression for this function.

• Write a minimal AND-NOR two-level expression for this function.

• Write a minimal NAND-AND two-level expression for this function.

• Write an XNF expression for this function.

2. Boolean Functions, Truth Tables, Logic Minimization, Two-Level Forms Consider a boolean function f(a, b, c, d). Suppose that the function is 1 if

• There is a single 1 among the inputs, or

• There is a single 0 among the inputs, or

and it is 0 otherwise.

(a) Write down a truth table for the function

(b) Using a Karnaugh map, provide a minimal sum-of-products (AND-OR) expression.

(d) Provide a minimal OR-NAND expression

(e) Provide a minimal NOR-OR expression

(f) Provide a minimal AND-NOR expression

(g) Provide an XNF expression.

3. Design of an Arbitrary Boolean Function with Constraints

Design a 4-variable Boolean function G(W, X, Y, Z) such that: G = 1 when the binary representation of W XY Z is a prime number, and 0 otherwise.

(a) List the prime numbers represented in binary by four variables W, X, Y, Z.

(b) Determine the minimal SOP (Sum of Products) form of G using a Karnaugh map.

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EE 2301 Introduction to Digital Systems Design

Hello, if you have any need, please feel free to consult us, this is my wechat: wx91due

EE 2301 Introduction to Digital Systems Design Fall 2024 Homework 2

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