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How does a Computer Add ?

This article explains how A, AND, OR gates work together within chips to perform logical operations and create adder circuits for binary addition. It covers the functions and outputs of XOR gates, simple adder circuits, and full adder circuits, providing a comprehensive guide to computer arithmetic.

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How does a Computer Add ?

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  1. How does a Computer Add ? A A AND Gate Output OR Gate Output B B Logic Gates within chips: B Output B Output A A 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 1 1 1 1 1 1 1 1

  2. Exclusive OR gate: A XOR Gate Output B B Output A 0 0 0 1 1 0 1 0 1 0 1 1

  3. Simple Adder Circuit: 0 XOR Gate Output = 0 + 0 AND Gate 0 Carry over = 0 0 1 XOR Gate Output = 1 + 0 1 AND Gate Carry over = 0 0

  4. Simple Adder Circuit: 0 XOR Gate Output = 1 + 1 0 AND Gate Carry over = 0 1 1 XOR Gate Output = 0 + 1 AND Gate 1 Carry over = 1 1

  5. Full Adder circuit 0 + 0, carry = 0 Carry over input = 0 0 XOR Gate Output = 0 0 0 AND Gate 0 0 0 XOR Gate + 0 Carry over = 0 0 OR Gate 0 AND Gate 0 0

  6. Full Adder circuit 0+1, carry = 0: Carry over input = 0 0 XOR Gate Output = 1 1 0 AND Gate 0 1 1 XOR Gate + 0 Carry over = 0 0 OR Gate 1 AND Gate 0 0

  7. Full Adder circuit 1+0, carry = 1: Carry over input = 1 1 XOR Gate Output = 0 1 1 AND Gate 1 1 1 XOR Gate + 0 Carry over = 1 1 OR Gate 1 AND Gate 0 0

  8. Multi-Bit Adder: C. C. C. C. X Y Z X . Y . Z . X Y Z X Y Z C.

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