Shannon Expansion

1
Shannon Expansion

• Given Boolean expression
• F w2 w1w3 w1w3
• Shannon Expansion of F on a variable, say w2, is
  to write F as two parts
• F w2(part0) w2(part1), where part0 is F with
  w2 0, and part1 is F with w2 1.
• It is a way to write F as sum of min terms.

2
6.2
3
6.3
4
6.7
5
6.11
6
6.16
7
6.20

• module m(f, w0, w1, w2)
• input w0, w1, w2
• output f
• wire t1, t2, t3 // wire declaration is
  optional
• decoder_3_8 D1 (x0, x1, x2, x3, x4, x5, x6,
  x7, w0, w1, w2, 1)
• or (t1, x1, x2) or (t2, x3, x5)
• or (t3, t1, t2), or (f, t3, x6)
• endmodule

8
Assume Following Decoder

• module decoder_3_8 (x0, x1, x2, x3, x4, x5, x6,
  x7, w0, w1, w2, en)
• input w0, w1, w2, en
• output x0, x1, x2, x3, x4, x5, x6, x7
• assign x0 ((en1) ? ((w0)(w1)(w2))
  0
• assign x1 ((en1) ? ((w0)(w1)w2)) 0
• endmodule

9
6.23

• module encoder_8_3 (w2, w1, w0, z, x7, x6, x5,
  x4, x3, x2, x1, x0)
• input x7, x6, x5, x4, x3, x2, x1, x0
• output w2, w1, w0, z
• assign w2,w1,w0,z
• (x7 ? 4b1110 (x6 ? 4b1100
• (x5 ? 4b1010 (x4 ? 4b1000
• (x3 ? 4b0110 (x2 ? 4b0100
• (x1 ? 4b0010 (x0 ? 4b0001
  4b0001))))))))
• endmodule