I'm currently trying to learn how binary adders work, but I don't understand what a "carry in" is for. What is the purpose of a "carry in"?
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asked Jul 23, 2015 at 23:32
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3 Answers
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It's important to understand there's a difference between a half-adder and a full-adder.
A half-adder is the simplest. It has 2 inputs and 2 outputs. It's basically a XOR.
The primary output is only 1 if one of both inputs is 1, but not if both are 1. That's Sum. The second output is only 1 if both inputs are 1. That's Carry.
That's nice, but only if you're adding two bits. If you need more bits, you'll have to combine some adders together. Here's where full-adders come into play. The Least Significant Adder is a half-adder, and every More Significant Adder will be a full-adder which will take the Carry of the previous adder.
A B Cin Cout Sum
0 0 0 0 0
1 0 0 0 1
0 1 0 0 1
1 1 0 1 0
0 0 1 0 1
1 0 1 1 0
0 1 1 1 0
1 1 1 1 1
(shamelessly copied from Wikipedia)
If Carry in is 0, the behaviour of a full-adder is identical to a half-adder.
However, if Carry in is 1, the behaviour of Sum is inversed and the behaviour of Carry out changes into a OR. As long as any of the inputs is 1, Carry out is 1.
Carry in is required to turn a basic 2-bit adder into a multiple-bit counter. That's the purpose of Carry in.
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1\$\begingroup\$ With twos complement format (-x == ~x + 1), the carry-in can also be used for subtraction (inverting the subtrahend and setting the carry-in negates the value which can then be added). \$\endgroup\$– user15426Commented Jul 24, 2015 at 0:21
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\$\begingroup\$ @PaulA.Clayton Technically that would be a subtractor. I had the idea that would provide an information overload for OP, there is much more information to share about this matter. \$\endgroup\$– MastCommented Jul 24, 2015 at 0:32
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1\$\begingroup\$ Avoiding info-dumps can be difficult for some people (like me); your judgment is probably correct. \$\endgroup\$– user15426Commented Jul 24, 2015 at 3:06
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Besides what is said by those who replied earlier, Carry can also mean an input coming from the flag register that allows linking one sum on a ALU to the next one. By linking I mean that, if your computer architecture has a ALU with a word size of 8 bits and you need to do a 16 bit sum, the ALU can use the Carry flag, placing it on its carry in as a way to allow the processor to continue the sum from the previous one. This allows two 8 bit sums to become a single two step 16bit sum.
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The purpose of the "carry" in is to accept the "carry" out of the previous adder. Carry works just like normal arithmetic.