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ํŽ˜์ด์ง€ ๋งจ ์œ„๋กœ ์˜ฌ๋ผ๊ฐ€๊ธฐ

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๋„คํŠธ์›Œํฌ ๊ด€์ ์—์„œ์˜ ํด๋ผ์šฐ๋“œ ์ปดํ“จํŒ…์„ ๊ณต๋ถ€ํ•˜๋Š” ์ค‘์ž…๋‹ˆ๋‹ค :)

[Computing System] ๋ถˆ ๋…ผ๋ฆฌ(Boolean Logic)

  • 2023.06.24 01:51
  • ๊ฒ…๋ถ€๊ฒ…๋ถ€๐Ÿ™ƒ/Computing System
๊ธ€ ์ž‘์„ฑ์ž: caputdraconis
๋ฐ˜์‘ํ˜•

๋ชจ๋“  ๋””์ง€ํ„ธ ๊ธฐ๊ธฐ๋Š” ๋ชจ๋‘ ์ •๋ณด๋ฅผ ์ €์žฅํ•˜๊ณ  ์ฒ˜๋ฆฌํ•˜๋„๋ก ์„ค๊ณ„๋œ ์นฉ๋“ค์€ ํƒ‘์žฌํ•˜๋Š”๋ฐ, ์ด ์นฉ๋“ค์€ ๋™์ผํ•œ ๊ตฌ์„ฑ ์š”์†Œ์ธ ๊ธฐ์ดˆ ๋…ผ๋ฆฌ ๊ฒŒ์ดํŠธ๋กœ ๋งŒ๋“ค์–ด์ง‘๋‹ˆ๋‹ค. ์ด๋ฒˆ ๊ธ€์—์„œ๋Š” ๊ฐ€์žฅ ๊ธฐ์ดˆ์ ์ธ ๋…ผ๋ฆฌ ๊ฒŒ์ดํŠธ์ธ Nand ๋ฅผ ์ด์šฉํ•˜์—ฌ ๋ถˆ ๊ฒŒ์ดํŠธ(Boolean Gate)๋ฅผ ๋งŒ๋“ค ๊ฒƒ์ž…๋‹ˆ๋‹ค. ๋ถˆ ๊ฒŒ์ดํŠธ๋ž€ ๋ถˆ ํ•จ์ˆ˜(Boolean Function)๋ฅผ ๋ฌผ๋ฆฌ์ ์œผ๋กœ ๊ตฌํ˜„ํ•œ ๊ฒƒ์ž…๋‹ˆ๋‹ค.

 

๋ถˆ ๋Œ€์ˆ˜

์ฐธ/๊ฑฐ์ง“, 1/0, ์˜ˆ/์•„๋‹ˆ์˜ค, ์ผœ์ง/๊บผ์ง ๊ฐ™์€ ์ด์ง„์ˆ˜ ๊ฐ’์„ ๋‹ค๋ฃจ๋Š” ๋Œ€์ˆ˜ํ•™์ž…๋‹ˆ๋‹ค. ๋ถˆ ํ•จ์ˆ˜๋Š” ์ด์ง„์ˆ˜๋ฅผ ์ž…๋ ฅ๋ฐ›์•„ ์ด์ง„์ˆ˜๋ฅผ ์ถœ๋ ฅํ•˜๋Š” ํ•จ์ˆ˜์ž…๋‹ˆ๋‹ค. ์ปดํ“จํ„ฐ๋Š” ์ด์ง„์ˆ˜๋ฅผ ํ‘œํ˜„ํ•˜๊ณ  ์ฒ˜๋ฆฌํ•˜๋Š” ํ•˜๋“œ์›จ์–ด์ด๋ฏ€๋กœ, ๋ถˆ ํ•จ์ˆ˜๋Š” ํ•˜๋“œ์›จ์–ด ์•„ํ‚คํ…์ฒ˜์˜ ์ค‘์‹ฌ์ ์ธ ์—ญํ• ์„ ์ˆ˜ํ–‰ํ•ฉ๋‹ˆ๋‹ค. ๊ทธ๋Ÿฌ๋ฏ€๋กœ, ๋ถˆ ํ•จ์ˆ˜๋ฅผ ์ •์˜ํ•˜๊ณ  ๋ถ„์„ํ•˜๋Š” ๊ฒƒ์ด ์ปดํ“จํ„ฐ ์•„ํ‚คํ…์ฒ˜๋ฅผ ๊ตฌ์ถ•ํ•˜๋Š” ์ฒซ ๋‹จ๊ณ„๊ฐ€ ๋ฉ๋‹ˆ๋‹ค. ๋ถˆ ํ•จ์ˆ˜๋ฅผ ์ •์˜ํ•˜๋Š” ๊ฐ€์žฅ ์‰ฌ์šด ๋ฐฉ๋ฒ•์œผ๋กœ๋Š” ์ง„๋ฆฌํ‘œ ํ‘œํ˜„์ด ์žˆ์Šต๋‹ˆ๋‹ค. ์ง„๋ฆฌํ‘œ ํ‘œํ˜„์€ ํ•จ์ˆ˜์˜ ์ž…๋ ฅ๊ฐ’๋“ค๊ณผ ๊ฒฐ๊ณผ๊ฐ’์„ ๋‚˜๋ž€ํžˆ ์“ฐ๋Š” ๋ฐฉ๋ฒ•์ž…๋‹ˆ๋‹ค. ์•„๋ž˜์˜ ํ‘œ๋Š” ์ง„๋ฆฌํ‘œ ํ‘œํ˜„์˜ ์˜ˆ์‹œ์ž…๋‹ˆ๋‹ค.

x y z f(x, y, z)
0 0 0 0
0 0 1 0
0 1 0 1
0 1 1 0
1 0 0 1
1 0 1 0
1 1 0 1
1 1 1 0

 

๋ถˆ ํ•จ์ˆ˜๋Š” ์ž…๋ ฅ๊ฐ’์— ๋Œ€ํ•œ ๋ถˆ ์—ฐ์‚ฐ์œผ๋กœ๋„ ํ‘œํ˜„ ๊ฐ€๋Šฅํ•ฉ๋‹ˆ๋‹ค. ์ž์ฃผ ์‚ฌ์šฉ๋˜๋Š” ๋ถˆ ์—ฐ์‚ฐ์€ ์•„๋ž˜์™€ ๊ฐ™์Šต๋‹ˆ๋‹ค.

  • And : x And y(x์™€ y๊ฐ€ ๋‘˜ ๋‹ค 1 ์ผ ๋•Œ๋งŒ 1). $xy$ ๋กœ ํ‘œํ˜„๋ฉ๋‹ˆ๋‹ค.
  • Or : x Or y(x ๋˜๋Š” y๊ฐ€ 1์ด๊ฑฐ๋‚˜, ๋‘˜ ๋‹ค 1์ผ ๋•Œ๋งŒ 1). $x + y$ ๋กœ ํ‘œํ˜„๋ฉ๋‹ˆ๋‹ค.
  • Not : Not x(x ๊ฐ€ 0์ผ ๋•Œ 1). $\bar{x}$ ์™€ ๊ฐ™์ด ํ‘œํ˜„๋ฉ๋‹ˆ๋‹ค.

์œ„์˜ ์ง„๋ฆฌํ‘œ ํ‘œํ˜„์— ์ •์˜๋œ ํ•จ์ˆ˜๋Š” $f(x, y, z) = (x+y)*\bar{z}$ ๋ผ๋Š” ๋ถˆ ํ‘œํ˜„์‹๊ณผ ๊ฐ™์Šต๋‹ˆ๋‹ค.

 

๊ฒŒ์ดํŠธ ๋…ผ๋ฆฌ

๊ฒŒ์ดํŠธ(gate)๋Š” ๋ถˆ ํ•จ์ˆ˜๋ฅผ ๊ตฌํ˜„ํ•œ ๋ฌผ๋ฆฌ์  ์žฅ์น˜์ž…๋‹ˆ๋‹ค. n ๊ฐœ์˜ ๋ณ€์ˆ˜๋ฅผ ๋ฐ›์•„ m ๊ฐœ์˜ 2์ง„ ๊ฒฐ๊ณผ๊ฐ’์„ ๋ฐ˜ํ™˜ํ•˜๋Š” ๋ถˆ ํ•จ์ˆ˜ f๊ฐ€ ์žˆ์„ ๋•Œ, f๋ฅผ ๊ตฌํ˜„ํ•˜๋Š” ๊ฒŒ์ดํŠธ์—๋Š” n ๊ฐœ์˜ ์ž…๋ ฅ ํ•€๊ณผ m ๊ฐœ์˜ ์ถœ๋ ฅ ํ•€์ด ์žˆ๊ฒŒ ๋ฉ๋‹ˆ๋‹ค. ๋ณต์žกํ•œ ๊ฒŒ์ดํŠธ๋Š” ๊ธฐ์ดˆ์ ์ธ ๊ฒŒ์ดํŠธ๋“ค๋กœ ๊ตฌ์„ฑํ•  ์ˆ˜ ์žˆ์Šต๋‹ˆ๋‹ค. ๊ฐ€์žฅ ๋‹จ์ˆœํ•œ ํ˜•ํƒœ์˜ ๊ฒŒ์ดํŠธ๋“ค์€ ํŠธ๋žœ์ง€์Šคํ„ฐ(transistor) ๋ผ๊ณ  ๋ถˆ๋ฆฌ๋Š” ์•„์ฃผ ์ž‘์€ ์Šค์œ„์น˜ ์žฅ์น˜๋“ค์„ ํŠน์ •ํ•œ ๊ตฌ์กฐ๋กœ ์—ฐ๊ฒฐํ•˜์—ฌ ํŠน์ • ๊ธฐ๋Šฅ์„ ํ•˜๋„๋ก ๋งŒ๋“  ๊ฒƒ๋“ค์ž…๋‹ˆ๋‹ค.

 

 

์ˆ˜ํ–‰ํ•œ ๊ณผ์ œ๋Š” ์•„๋ž˜์˜ ๋ ˆํฌ์ง€ํ† ๋ฆฌ์—์„œ ํ™•์ธ ๊ฐ€๋Šฅํ•ฉ๋‹ˆ๋‹ค.

https://github.com/caputdraconis050630/ABC

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