## Boolean expression for sum bit of full adder

The Boolean expression I find on the internet for the sum bit of a full adder is A xor B xor Cin. Does’t this expression exclude the A=1,B=1,Cin=1 situation? When that happens, the sum bit is also 1, isn’t it?

Thank you very much.

I recently came across carry look-ahead adder(CLA) in David and Sarah Harris’s book(Digital Design and Computer Architecture). The circuitry for a 64 bit number (standard integer size in C) is probably huge and gets very complicated.The generate function has just too many gates.

My question is: are CLAs used in current processors such as the Intel i3 or in similar series? Also, are there any better implementations of carry adders?

I am aware of the fact that older processors like the Intel 8008 and the kind did use a CLA.

## How do I get the NAND gate configuration for full adder from the logic table?

I’m self-studying, but I’ve gotten stuck already. If I’m given the logic table for a full-adder or any two-output table, how do I figure out the NAND-gate configuration, preferably methodically? Specifically, given the table:

``x y z | 2^1 2^0 0 0 0 |  0   0 1 0 0 |  0   1 0 1 0 |  0   1 0 0 1 |  0   1 1 1 0 |  1   0 0 1 1 |  1   0 1 0 1 |  1   0 1 1 1 |  1   1 ``

How do I find the following set-up:

So far, I’ve gotten:

x’yz+xy’z+xyz’+xyz=x(yz’+y’z)+xy

xy’z’+x’yz’+x’y’z+xyz=x'(yz’+y’z)+x(y’z’+yz)

I can see the first XOR gate between A and B in the diagram and I can see the yz’+y’z XOR gate, but I’m not sure how to proceed from there.

This method add all numbers in list and return it as double

``public HashMap<String, Double> add(HashMap<String, List<? extends Number>> map){     HashMap<String, Double> result = new HashMap<>();      map.forEach((key, value) -> {         Double sum = 0.0;          for (Number num : value){             sum += num.doubleValue();         }          result.put(key, sum);     });     return result; } ``

Testing my method with different types

``public static void main(String[] args) {     Adder adder  = new Adder();     HashMap<String, List<? extends Number>> hashMap = new HashMap<>();      List<Integer> list1 = new ArrayList<>();     list1.add(1);     list1.add(2);     list1.add(3);      List<BigDecimal> list2 = new ArrayList<>();     list2.add(new BigDecimal("9.87654321e300"));     list2.add(new BigDecimal("987654321"));     list2.add(new BigDecimal("987654321"));       hashMap.put("list1", list1);     hashMap.put("list2", list2);      System.out.println(adder.add(hashMap));   } ``

Is there way to improve this?

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