Binary Addition: The Foundation of Computer Arithmetic
Master binary addition with carry propagation, half adders, full adders, and worked examples for computer arithmetic.
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Binary addition adds two binary numbers bit by bit with carry propagation. It follows four simple rules: 0+0=0, 0+1=1, 1+0=1, 1+1=10 (write 0, carry 1). Every arithmetic operation in a computer is ultimately built on binary addition.
Key Takeaway
Binary addition uses four rules and carry propagation. It is implemented in hardware using half adders and full adders.
1. The Four Rules
- 0 + 0 = 0
- 0 + 1 = 1
- 1 + 0 = 1
- 1 + 1 = 10 (write 0, carry 1)
2. Worked Example: 1011 + 1101
1011 (11) + 1101 (13) = 11000 (24). Carry propagates through all four columns.
3. Hardware: Half Adder and Full Adder
A half adder adds two bits (sum = XOR, carry = AND). A full adder adds three bits including carry input. Multi-bit addition uses ripple-carry or carry-lookahead adders.
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