Mantıksal Cebir

Mantıksal cebir, cebirden farklı olarak, lojik değişmeleri sembol eden bir metottur. Yalnız iki yönüyle farklıdır:

  1. Matematiksel olarak yapılan çalışmalar mantıksal cebirde yapılmamıştır.
  2. Bu yüzden mantıksal cebirde sayısal değerler gösterilmez, genellikle harf kullanılır.

Örnek olarak: Bir anahtar devresi açık veya kapalıdır.

Basit olarak bir cümle ya doğru, ya yanlıştır.

Değişkenleri

Basit bir mantığa sahiptir. Her mantıksal değişkenin tek değeri vardır. Doğru ve yanlış eş zamanlıdır.

Herhangi bir doğru değişkeni, diğer bir doğruyla eşleşir. Yine herhangi bir yanlış değişkeni, diğer bir yanlışla eşleşir. Yani doğru değişken yanlış değişkene eşlemez. Ve ikisinden sadece birisi söz konusudur.

Yazımı

Mantıksal cebirde, lojik devrelerin durumlarını ifade edilirken alfabetik harfler kullanılır. Örnek olarak; X harfinde bir değişken ele alalım. Bu doğru veya yanlış olabilir. Yani eksiden artıya, artıdan eksiye herhangi bir değer gösterebilir.

Bunun tersi ele aldığımız ilk harfin barı, yani değilidir. Bar, X üzerinde sadece X'i kapsayan bir düz çizgiyle ifade edilir. Yani X değeri doğru iken; X'in barı yanlış, X değeri yanlış iken; X'in barı doğrudur. Deminde ifade ettiğim gibi değili, yani tersidir.

Bazı devrelerde doğru; H, bazılarınca T olarak gösterilir. H, İngilizcede yüksek manasına gelen High sözcüğünden, T ise doğru manasına gelen True sözcüğünden gelmektedir. Yanlış içinse; L veya F harfleri kullanılır. L, İngilizcede düşük manasına gelen Low sözcüğünden; F harfi ise İngilizcede yanlış manasına gelen False sözcüğünden gelir. Ayrıca T-F (True- False) programlama dillerinde özellikle döngülerde çok sık kullanılan terimlerdir.

İkilik sayı sistemi olan Binary sayı sistemi kolaylık açısından kullanılabilir. 0 değeri false, yani yanlış, 1 değeri true, yani doğrudur.

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