Examine the validity of Equations 9.1 by applying them to the last two columns in Table 9.1. Table 9.1 4-bit gray and natural binary codes Natural binary code (B,B,B,B,) Gray code- (G,G,G,G, Decimal Code Rotation Range (O 0-22.5 000 0000 1 22.5–45 0001 0001 45-67.5 0010 0011 3 67.5-90 0011 0010 4 90–112.5 0100 0110 112.5–135 0101 0111 6. 135–157.5 0110 0101 157.5–180 0111 0100 8 180–202.5 1000 1100 202.5–225 1001 1101 10 225-247.5 1010 1111 11 24 7.5–270 1011 1110 12 270–292.5 1100 1010 13 292.5–315 1101 1011 14 315-337.5 1110 1001 15 337.5–360 1111 1000 function. The Boolean expressions that relate the binary bits (B) to the gray code bits (G,) are B3 = G, B2 = B; © G, (9.1) B1 = B2 ® G, Bo = B, O G.
Examine the validity of Equations 9.1 by applying them to the last two columns in Table 9.1. Table 9.1 4-bit gray and natural binary codes Natural binary code (B,B,B,B,) Gray code- (G,G,G,G, Decimal Code Rotation Range (O 0-22.5 000 0000 1 22.5–45 0001 0001 45-67.5 0010 0011 3 67.5-90 0011 0010 4 90–112.5 0100 0110 112.5–135 0101 0111 6. 135–157.5 0110 0101 157.5–180 0111 0100 8 180–202.5 1000 1100 202.5–225 1001 1101 10 225-247.5 1010 1111 11 24 7.5–270 1011 1110 12 270–292.5 1100 1010 13 292.5–315 1101 1011 14 315-337.5 1110 1001 15 337.5–360 1111 1000 function. The Boolean expressions that relate the binary bits (B) to the gray code bits (G,) are B3 = G, B2 = B; © G, (9.1) B1 = B2 ® G, Bo = B, O G.
Computer Networking: A Top-Down Approach (7th Edition)
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Chapter1: Computer Networks And The Internet
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Transcribed Image Text:I CLASS DISCUSSION ITEM 9.5
Gray-to-Binary-Code Conversion
Examine the validity of Equations 9.1 by applying them to the last two columns in
Table 9.1.
Table 9.1 4-bit gray and natural binary codes
Natural binary
code (B,B,B,B,)
Gray code
(G,G,G,G,)
Decimal Code
Rotation Range (*)
0-22.5
0000
0000
0001
1
22.5-45
0001
45-67.5
0010
0011
67.5–90
0011
0010
90–112.5
0110
0111
4
0100
112.5–135
135–157.5
157.5–180
0101
6
0110
0101
0111
0100
180–202.5
1000
1100
202.5–225
1001
1101
10
225–247.5
1010
1111
11
24 7.5–270
1011
1110
12
270–292.5
1100
1010
13
292.5–315
1101
1011
14
315–337.5
1110
1001
15
337.5-360
1111
1000
function. The Boolean expressions that relate the binary bits (B) to the gray code
bits (G) are
B3 = G3
B, = B3© G,
(9.1)
B1 = B, © G|
Bo = B, O Go
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