Question

Decimal Binary Gray code Y3:0 0 0000 0000 1 0001 0001 2 0010 0011 3 0011 0010 4 0100 0110 5 0101 0111 6 0110 0101 7 0111 0100 8 1000 1100 9 1001 1101 10 1010 1111 11 1011 1110 12 1100 1010 13 1101 1011 14 1110 1001 15 1111 1000 clk Gray code circuit Y3 Y2 Y1 Yo Half Adder 13 12 11 10 clr 4-bit register Q3 Q2 Q1 Q0 A B Cout + S XOR A B- Y Y = A \oplus B

          Decimal Binary Gray code
Y3:0
0 0000 0000
1 0001 0001
2 0010 0011
3 0011 0010
4 0100 0110
5 0101 0111
6 0110 0101
7 0111 0100
8 1000 1100
9 1001 1101
10 1010 1111
11 1011 1110
12 1100 1010
13 1101 1011
14 1110 1001
15 1111 1000
clk Gray
code
circuit Y3
Y2
Y1
Yo
Half
Adder
13 12 11 10
clr
4-bit register
Q3 Q2 Q1 Q0
A
B
Cout
+
S
XOR
A
B-
Y
Y = A \oplus B

Decimal Binary Gray code
Y3:0
0 0000 0000
1 0001 0001
2 0010 0011
3 0011 0010
4 0100 0110
5 0101 0111
6 0110 0101
7 0111 0100
8 1000 1100
9 1001 1101
10 1010 1111
11 1011 1110
12 1100 1010
13 1101 1011
14 1110 1001
15 1111 1000
clk Gray
code
circuit Y3
Y2
Y1
Yo
Half
Adder
13 12 11 10
clr
4-bit register
Q3 Q2 Q1 Q0
A
B
Cout
+
S
XOR
A
B-
Y
Y = A ⊕B

Added by Francisco S.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Varsha Aggarwal

Step 1

To do this, we can use a 4-bit resettable register to store the current Gray code value. The register will have four inputs (Y3, Y2, Y1, Y0) and four outputs (Q3, Q2, Q1, Q0). Show more…

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Gray code is an ordering of the binary numbers such that two successive values differ in one bit only. The 4-bit gray code is given in the table below. The Gray code for decimal 15 rolls over to decimal 0 with only one bit change. This is called the "cyclic" property of a Gray code. Design a digital circuit that produces 4-bit Gray code on consecutive clock cycles. You are allowed to use only one 4-bit resettable register, four half adders, and three 2-bit XOR gates. Sketch the circuit schematic of your design by using the symbols given below. Gray code Decimal Binary Y3:0 0 0000 1 0001 2 0011 3 0010 4 0110 5 0111 6 0101 7 0100 8 1100 9 1101 10 1111 11 1110 12 1010 13 1011 14 1001 15 1000