Adder and multiplexer
The usual combinational circuits: half adder, full adder, ripple-carry adder, multiplexer, demultiplexer, decoder and their place in the arithmetic logic unit.
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A few cards from the deck
Combinational circuit: what is it?
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A circuit of gates whose outputs depend only on the current inputs, with no memory of what happened before.
The same input combination always gives the same output, after the gates' propagation delay. As soon as a circuit keeps a state, it becomes sequential.
A full adder receives A = 1, B = 1 and a carry in of 1. What are the sum S and the carry out?
- S = 1 and carry = 1
- S = 0 and carry = 1
- S = 1 and carry = 0
- S = 0 and carry = 0
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S = 1 and carry = 1
1 + 1 + 1 = 3, which is 11 in binary: the low bit (1) is the sum, the high bit (1) is the carry out.
In a half adder, the sum is an … of A and B, and the carry is an … of A and B.
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In a half adder, the sum is an XOR of A and B, and the carry is an AND of A and B.
1 + 1 = 10 in binary: the sum is 0 (XOR) and the carry is 1 (AND). In the other three cases the carry is zero.
Half adder: what is it?
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A circuit that adds two bits A and B and returns their sum and a carry out, with no carry input.
Sum = A ⊕ B and carry = A · B: one XOR and one AND. It suffices for the lowest bit, but not for the next ones, which receive a carry.