Basic Logic Gates in Computer Science
The foundational blocks of digital logic, including AND, OR, NOT, NAND, NOR, EX-OR gates, and Half Adder operation. Dive into truth tables and circuit realizations.
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BY GAWARE S.R. COMPUTER SCIENCE DEPARTMENT
Basic Logic Gates Logic gates constitute the foundation blocks for digital logic. Let us start by reviewing these gates and their truth tables: 1. AND Gate An AND Gate has two or more inputs and produces one output as follows: output = 1 if all of the inputs are high, output = 0 if one or more of the inputs are low [1]. An OR gate also has two or more inputs and produces one output as follows: output = 1 if one or more inputs are high, output = 0 if all inputs are low [1]:
2. OR Gate: An OR gate also has two or more inputs and produces one output as follows: output = 1 if one or more inputs are high, output = 0 if all inputs are low [1]:
3.NOT Gate: The inverter gate has one input and produces one output as follows: output =1 if input is low, output = 0 if input is high [1]. 4. The NAND gate has two or more inputs and produces one output as follows: output = 0 if all the inputs are high, output = 1 if any of the inputs are low [1]
5. NOR Gate: The NOR gate has two or more inputs and produces one output as follows: output = 1 if all inputs are low, output = 0 if any of the inputs is high [1]. 6. EX-OR Gate: The Exclusive-OR gate always has two inputs only and produces one output as follows: output = 1 when inputs are not similar, output = 0 when inputs are the same [1].
7. EX-NOR Gate: The Exclusive-NOR gate always has two inputs only and produces one output as follows: output = 1 when inputs are both high or are both low, output = 0 when inputs are not similar [1].
Half Adder: Adding two single-bit binary values X, Y produces a sum S bit and a carry out C-out bit. This operation is called half addition and the circuit to realize it is called a half adder. TRUTH TABLE X X 0 0 1 1 Y Y 0 1 0 1 SUM 0 1 1 0 SUM CARRY 0 0 0 1 CARRY SYMBOL
S (X,Y) = (1,2) S = X'Y + XY' S = XY CARRY(X,Y) = (3) CARRY = XY CIRCUIT
Full Adder Full adder takes a three-bits input. Adding two single-bit binary values X, Y with a carry input bit C-in produces a sum bit S and a carry out C-out bit. Truth Table X 0 0 0 0 1 1 1 1 Y 0 0 1 1 0 0 1 1 Z 0 1 0 1 0 1 0 1 SUM 0 1 1 0 1 0 0 1 CARRY 0 0 0 1 0 1 1 1
