13 - Full adders

 1. The full adder is usually a component in a cascade of adders, which add 8, 16, 32, etc. bit binary numbers. The circuit produces a _______________

  eight bit (byte) output

  two-bit output

  one-bit output

  output that is always 'high' or 1

 2. A full adder is a logical circuit that performs an addition operation on three one-bit binary numbers. The full adder produces a sum of the three inputs and carry value



 3. A full adder can be combined with other full adders or work on its own.



 4. The main difference between a half-adder and a full-adder is that the full-adder has __________________________

  three inputs and two outputs.

  a single input and a single output

  multiple (up to 3 billion) inputs and a single output

  two inputs and one output

 5. Full adder: The first two inputs are A and B and the third input is an input carry that is sometimes designated as CIN



 6. In the following truth table for a full adder, the CIN and COUT stand for:

  CIN = 1 and COUNT = CIN + 1

  total carry count (for inputs) and total count + 1

  CIN = input carry and COUT = output + CIN

  input carry and output carry

 7. Analyse the following diagram for a full adder. We can see that the output S is an _____ between the input A and the half-adder SUM output with B and CIN inputs





 8. Looking at the circuit diagram, COUT will only be true if any of the two inputs out of the three are LOW.



 9. Read the excerpt on full adders below and fill in the blanks
It is possible to implement a full adder circuit
with the help of two half adder circuits. 

The first half adder will be used to add 
A and B to produce a partial Sum. 

The second half adder logic can be used to _

If any of the half adder logic
produces a carry, there will be an output carry. 

Thus, COUT will be an OR function of the half-adder carry outputs.

  add the SUM to the final S output

  produce the final SUM by adding 1 to whatever the output is

  add the SUM to the first output produced and get the CIN output

  add CIN to the Sum produced by the first half adder to get the final S output.

 10. We want to be able to add two single bit numbers and also an incoming carry bit. In other words we effectively want to add ____________________
Note: This is where full adders are very useful

  three single bit numbers

  three double bit numbers

  eight single bit numbers

  four single bit binary 1s

 11. For three binary bits there are ______ possible combinations





 12. Combining two half adders will produce a full adder without the need for any additional circuitry



 13. The full adder is able to add three 1 bit numbers, the third bit is usually the ______________________

  final sum

  carry bit from the previous adder.

  SUM of the half adder and OR gate

  1 that is the output from the first half adder

 14. Full adders can be ____________ to allow two numbers of any bit length to be added


  combined with up to four AND gates


  combined with a NAND gate

 15. Coders can make sure their code is monitoring the __________ in case their calculations are out of range.

  overflow flag

  low outputs (0s)


  high outputs (e.g 1s)