About Karnaugh Maps:

Some addtional notes on Gray codes and 5-bit K-maps

Consider the 4-bit K-map matrix:
(w, x, y, z)
Final Bits (y, z) - binary and decimal
00
01
11
10
Initial
Bits
(w, x)
00
0000 = 0
0001 = 1
0011 = 3
0010 = 2
01
0100 = 4
0101 = 5
0111 = 7
0110 = 6
11
1100 = 12
1101 = 13
1111 = 15
1110 = 14
10
1000 = 8
1001 = 9
1011 = 11
1010 = 10

w

Final Bits
00
01
11
10
Initial
Bits
00
0000
0001
0011
0010
01
0100
0101
0111
0110
11
1100
1101
1111
1110
10
1000
1001
1011
1010

w'

Final Bits
00
01
11
10
Initial
Bits
00
0000
0001
0011
0010
01
0100
0101
0111
0110
11
1100
1101
1111
1110
10
1000
1001
1011
1010

x

Final Bits
00
01
11
10
Initial
Bits
00
0000
0001
0011
0010
01
0100
0101
0111
0110
11
1100
1101
1111
1110
10
1000
1001
1011
1010

x'

Final Bits
00
01
11
10
Initial
Bits
00
0000
0001
0011
0010
01
0100
0101
0111
0110
11
1100
1101
1111
1110
10
1000
1001
1011
1010

y

Final Bits
00
01
11
10
Initial
Bits
00
0000
0001
0011
0010
01
0100
0101
0111
0110
11
1100
1101
1111
1110
10
1000
1001
1011
1010

y'

Final Bits
00
01
11
10
Initial
Bits
00
0000
0001
0011
0010
01
0100
0101
0111
0110
11
1100
1101
1111
1110
10
1000
1001
1011
1010

z

Final Bits
00
01
11
10
Initial
Bits
00
0000
0001
0011
0010
01
0100
0101
0111
0110
11
1100
1101
1111
1110
10
1000
1001
1011
1010

z'

Final Bits
00
01
11
10
Initial
Bits
00
0000
0001
0011
0010
01
0100
0101
0111
0110
11
1100
1101
1111
1110
10
1000
1001
1011
1010

xz

Final Bits
00
01
11
10
Initial
Bits
00
0000
0001
0011
0010
01
0100
0101
0111
0110
11
1100
1101
1111
1110
10
1000
1001
1011
1010

x'z'

Final Bits
00
01
11
10
Initial
Bits
00
0000
0001
0011
0010
01
0100
0101
0111
0110
11
1100
1101
1111
1110
10
1000
1001
1011
1010

xy

Final Bits
00
01
11
10
Initial
Bits
00
0000
0001
0011
0010
01
0100
0101
0111
0110
11
1100
1101
1111
1110
10
1000
1001
1011
1010

wx

Final Bits
00
01
11
10
Initial
Bits
00
0000
0001
0011
0010
01
0100
0101
0111
0110
11
1100
1101
1111
1110
10
1000
1001
1011
1010

wxy'

Final Bits
00
01
11
10
Initial
Bits
00
0000
0001
0011
0010
01
0100
0101
0111
0110
11
1100
1101
1111
1110
10
1000
1001
1011
1010

w'yz

Final Bits
00
01
11
10
Initial
Bits
00
0000
0001
0011
0010
01
0100
0101
0111
0110
11
1100
1101
1111
1110
10
1000
1001
1011
1010

w'yz

Final Bits
00
01
11
10
Initial
Bits
00
0000
0001
0011
0010
01
0100
0101
0111
0110
11
1100
1101
1111
1110
10
1000
1001
1011
1010

wx'yz'

Final Bits
00
01
11
10
Initial
Bits
00
0000
0001
0011
0010
01
0100
0101
0111
0110
11
1100
1101
1111
1110
10
1000
1001
1011
1010

w'x'yz

Final Bits
00
01
11
10
Initial
Bits
00
0000
0001
0011
0010
01
0100
0101
0111
0110
11
1100
1101
1111
1110
10
1000
1001
1011
1010


Gray Codes - From Carpinelli, page 9

New Gray codes are produced by taking the previous, appening the list reversed, and putting 0's before the first half and 1's before the second half, thus:
Bits: 
0 1 2 3 4 5
--------------------------------------
0 0 00 000 0000 00000
1 01 001 0001 00001

11 011 0011 00011
10 010 0010 00010

110 0110 00110
111 0111 00111
101 0101 00101
100 0100 00100

1100 01100
1101 01101
1111 01111
1110 01110
1010 01010
1011 01011
1001 01001
1000 01000

11000
11001
11011
11010
11110
11111
11101
11100
10100
10101
10111
10110
10010
10011
10001
10000

5-Bit K-Maps - not quite so useful


(v, w, x, y, z)
Final Bits (y, z) - binary and decimal
00
01
11
10
Initial
Bits
(v, w, x)
000
00000 = 0
00001 = 1
00011 = 3
00010 = 2
001
00100 = 4
00101 = 5
00111 = 7
00110 = 6
011
01100 = 12
01101 = 13
01111 = 15
01110 = 14
010
01000 = 8
01001 = 9
01011 = 11
01010 = 10
110
11000 = 24
11001 = 25
11011 = 26
11010 = 26
111
11100 = 28
11101 = 29
11111 = 31
11110 = 30
101
10100 = 20
10101 = 21
10111 = 23
10110 = 22
100
10000 =16 10001 = 17
10011 = 19
10010 = 18

This representation is nice in v, w, y and z, but expression involving x are not so nice, see the following example:

x'z'

Final Bits (y, z) - binary and decimal
00
01
11
10
Initial
Bits
(v, w, x)
000
00000 = 0
00001 = 1
00011 = 3
00010 = 2
001
00100 = 4
00101 = 5
00111 = 7
00110 = 6
011
01100 = 12
01101 = 13
01111 = 15
01110 = 14
010
01000 = 8
01001 = 9
01011 = 11
01010 = 10
110
11000 = 24
11001 = 25
11011 = 26
11010 = 26
111
11100 = 28
11101 = 29
11111 = 31
11110 = 30
101
10100 = 20
10101 = 21
10111 = 23
10110 = 22
100
10000 =16 10001 = 17
10011 = 19
10010 = 18