Page 13 - INTRODUCTION_TO_LOGIC CIRCUITS_Neat

Digital Logic Circuits 7

BASIC IDENTITIES OF

[1] x + 0 = x [2] x •
[3] x + 1 = 1 [4] x •
[5] x + x = x [6] x •
[7] x + x’ = 1 [8] x •
[9] x + y = y + x [10] xy =
[11] x + (y + z) = (x + y) + z [12] x(yz
[13] x(y + z) = xy +xz [14] x +
[15] (x + y)’ = x’y’ [16] (xy)
[17] (x’)’ = x

Usefulness of this Table
- Simplification of the Boolean fun
- Derivation of equivalent Boolean
to obtain logic diagrams utilizing
-- Ordinarily ANDs, ORs, and Inve
-- But a certain different form of B
to obtain circuits with NANDs o
→ Applications of De Morgans

x’y’ = (x + y)’ x’+
I, AND → NOR I, O

Computer Organization