Question

Click Submit to complete this assessment Questions 10 points Design a digital circuit that reorders the bits of a 4-bit binary number as follows: If the number is even, bits by bb bby become b, bobby. For example, 0110 becomes 1001 If the number is odd, bits bybb, b, bbecome bybob. For example, 1001 becomes 0110 Solve the following on paper, and then fill in the blanks below: NOTE: In parts 3 and 4, there is no need to draw the wires, you can assign inputs to gates directly. You can use the variables in complemented or uncomplemented form, ie, you can assign A or A' as input to any gate directly. You can also use gates with any number of inputs. 1) Construct the truth table. Label your inputs (A, B, C, D) and your outputs (W.X Y Z) in this order. 2) Use K-Maps to get the minimized expressions 3) Implement the circuit using logic gates. 4) Show an equivalent implementation using NAND gates only, Fill in the blanks: What is the Boolean expression for W? What is the Boolean expression for X? What is the Boolean expression for ? What is the Boolean expression for Z?

Answer 1

(a.) According to the question the truth table will be designed as follows:-

a	b	c	d	W	X	Y	Z
0	0	0	0	0	0	0	0
0	0	0	1	0	0	1	0
0	0	1	0	1	0	0	0
0	0	1	1	0	0	1	1
0	1	0	0	0	0	0	1
0	1	0	1	1	0	1	0
0	1	1	0	1	0	0	1
0	1	1	1	1	0	1	1
1	0	0	0	0	0	1	0
1	0	0	1	0	1	1	0
1	0	1	0	1	0	1	0
1	0	1	1	0	1	1	1
1	1	0	0	0	0	1	1
1	1	0	1	1	1	1	0
1	1	1	0	1	0	1	1
1	1	1	1	1	1	1	1

(b.) Using k-map the minimized expression is derived as follows:-

abled 00 ol 11 Jo a6 cd 00 ol 10 3 3 2 3 2 1 Ol 1 S 7 16 ol - 4 ५ s 7 6. 12 1 1 13 104 12 13 14 10 o 8 a 10 W = cd'+bd X = ad cd To cd at cub 11 00 1 1 o 1 31 2. 31 2 ol 1 < 1 17 7 J ol 1 6 S' 7 1 1 6 1 ( / 12 11 12 IS 13 1 114 131 15 14 lo 10 B В. 9 Ito 3 g log Y= atd z = cdt o d'

(c.) The implementation of the circuit using logic gates are as follows:-

с C D d' W b ь d о a d. Dr d С C d- C D Z b Ы d' -

(d.) The implementation of the circuit using NAND gates are as follows:-

с d' العام Do d d a-Dam с C d b d' Doz