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計算機概論Lab-1

Digital Logic

image

https://hackmd.io/@IMOK/Lab1

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講師: 賴昱有

Logic Gate

image

CREDIT:https://www.nutsvolts.com/magazine/article/small-logic-gates-spawn-big-dreams-part-1

訊號以二進位數字 0(false) 和 1(true)表示，對應於低電壓（0）和高電壓（1）。
數位邏輯利用邏輯閘（AND、OR、NOT ）來進行基本運算，
這三個邏輯閘可以組合成任何更複雜的邏輯電路，用於處理、計算和儲存數據。

AND GATE

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x y z
0 0 0
0 1 0
1 0 0
1 1 1

OR GATE

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x y z
0 0 0
0 1 1
1 0 1
1 1 1

NOT GATE

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x z
0 1
1 0

NOR GATE

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x y z
0 0 1
0 1 0
1 0 0
1 1 0

XOR GATE

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x y z
0 0 0
0 1 1
1 0 1
1 1 0

XNOR GATE

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x y z
0 0 1
0 1 0
1 0 0
1 1 1

image

HALF ADDER

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CREDIT : GITBOOK-HALF ADDER

1-bit 二進位的數字相加
結果以 S 表示
進位以 Cout 表示

A B S Cout
0 0 0 0
0 1 1 0
1 0 1 0
1 1 0 1

FULL ADDER

1-bit 二進位的數字相加
Cin 為前一步的進位
結果以 S 表示
進位以 Cout 表示

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CREDIT : GITBOOK-FULL ADDER

A B Cin S Cout
0 0 0 0 0
0 0 1 1 0
0 1 0 1 0
0 1 1 0 1
1 0 0 1 0
1 0 1 0 1
1 1 0 0 1
1 1 1 1 1

LogicCircuit Download URL:

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https://www.logiccircuit.org/download.html

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TIPS

  • crtl: multi select
  • shift: draw select
  • alt: split line

作業網站

作業做完請上傳到 http://140.121.197.13/tutorial
並且注意上傳時間限制、檔名、其他規範

上課時提前做完可以直接給助教 demo 登記
就不需要上傳 demo 過的部分

  1. 利用 LogicCircuit 畫出下圖的邏輯電路
    並產生出他的 Truth Table
    請注意接點位置及工整度
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  1. 利用 LogicCircuit 畫出下圖的 J-K flip flop
    並產生出他的 Truth Table
    請注意接點位置及工整度
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  1. 利用 LogicCircuit 畫出前面介紹過的 1-bit Full Adder並產生出他的 Truth Table請注意接點位置及工整度

  2. 結合上面的 1-bit Full Adder 做出 2-bit Full Adder

  3. (*) 結合上面的 2-bit Full Adder 做出 4-bit Full Adder

(不計分)

  1. 多 bit 的 Full Adder 被稱為 Ripple Carry Adder請查閱與 Carry Lookahead Adder 的差別
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