Given two three bit numbers a2a1a0 and b2b1b0 and c, the carry in, the…

GATE · 2006 · CS

Given two three bit numbers a2a1a0 and b2b1b0 and c, the carry in, the function that represents the carry generate function when these two numbers are added is:

1. A.

   a2b2 + a2a1b1 + a2a1a0b0 + a2a0b1b0 + a1b2b1 + a1a0b2b0 + a0b2b1b0

2. B.

   a2b2 + a2b1b0 + a2a1b1b0 + a1a0b2b1 + a1a0b2 + a1a0b2b0 + a2a0b1b0

3. C.

   a2 + b2 + (a2 ⊕ b2)(a1 + b1 + (a1 ⊕ b1)(a0 + b0))

4. D.

   a2b2 + ¬a2 a1b1 + ¬(a2a1)a0b0 + ¬a2 a0 ¬b1 b0 + a1 ¬b2 b1 + ¬a1 a0 ¬b2 b0 + a0 ¬(b2b1)b0

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