作者guessi (沒)
站內TransCSI
標題Re: [問題] 基本定理和卡諾圖化簡問題
時間Mon Dec 10 03:01:37 2007
※ 引述《rx10a (奶油濺兔)》之銘言：
: 以下有幾個問題在自修時讀不懂煩請朋友們解說 謝謝!
: Q1:(A) XY+YZ+X'Z=XY+X'Z (B)(X+Y)(Y+Z)(X'+Z)=(X+Y)(X'+Z)
: Q2:卡諾圖化簡請麻煩幫我舉例說明 謝謝 (光看書本化簡步驟不懂)
: Q3:(A) X(X+Y)=X+XY=X(1+Y)=X (B) (X+Y)(X+Z)=X+XZ+XY+YZ=X(1+Z+Y)+YZ=X+YZ
若有錯誤，煩請指教更正... 3Q
Q1-A: XY + YZ + X'Z = XY + X'Z
卡諾圖(左式) 卡諾圖(右式)
╲XY ╲XY
Z ╲ 00 01 11 10 Z ╲ 00 01 11 10
┌─┬─┬─┬─┐ ┌─┬─┬─┬─┐
0 │ │ │
１│ │ 0 │ │ │
１│ │
├─┼─┼
─┼─┤ ├─┼─┼
─┼─┤
1 │１│１│
１│ │
XY 1 │１│１│
１│ │
XY
└─┴─┴─┴─┘ └─┴─┴─┴─┘
╲XY
+ ╲XY
+
Z ╲ 00 01 11 10 Z ╲ 00 01 11 10
┌─┬─┬─┬─┐ ┌─┬─┬─┬─┐
0 │ │ │１│ │
===>> 0 │ │ │１│ │
├─┼─┼─┼─┤
===>> ├─┼─┼─┼─┤
1 │１│
１│１│ │
YZ 1 │
１│１│１│ │
X'Z
└─┴─┴─┴─┘ └─┴─┴─┴─┘
╲XY
+
Z ╲ 00 01 11 10
┌─┬─┬─┬─┐
0 │ │ │１│ │ 看圖應該就懂了... QQ
├─┼─┼─┼─┤
1 │
１│１│１│ │
X'Z
└─┴─┴─┴─┘
Q1-B: (X+Y)(Y+Z)(X'+Z)=(X+Y)(X'+Z)
(X+Y)(Y+Z)(X'+Z)
= (X+Y)(X'Y + YZ + X'Z + Z)
= (X+Y)(X'Y + Z(X' + Y + 1))
= (X+Y)(X'Y + Z)
= XX'Y + XZ + X'Y + YZ
= XX' + XZ + X'Y + YZ
= X'(X+Y) + Z(X+Y)
= (X+Y)(Z'+Z) ........#
Q2: 請參考Q1-A
Q3-A: X(X+Y)=X+XY=X(1+Y)=X
X(X+Y)
= XX + XY
= X + XY
= X．1 + X．Y
= X(1+Y)
= X(1)
= X ..........#
Q3-B: (X+Y)(X+Z) = X+XZ+XY+YZ = X(1+Z+Y)+YZ=X+YZ
(X+Y)(X+Z) ↑ ↑
= XX+XZ+YX+YZ │ │
=
X +
XZ +
XY + YZ ─┘ │
= X．1 + X．Z + X．Y + Y．Z │
= X(1 + Z + Y) + YZ ────────┘
= X + YZ .....#
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1F：→ chynlin:連圖都畫好，真好~~ 12/26 16:31