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12 - Half adders

 1. An adder is a digital logic circuit in electronics that implements addition of numbers
In many computers and other types of processors,
 adders are used to calculate addresses, similar 
operations and table indices in the ALU and also
 in other parts of the processors.
Halfadder.gif

  TRUE

  FALSE

 2. With the help of half adder, we can design circuits that are capable of performing _____________ with the help of logic gates.

  subtraction

  both addition and multiplication

  simple addition

  complex recursion

 3. From analysis of the below, it is clear that this 1-bit adder can be easily implemented with the help of XOR/EXOR Gate for the output ‘SUM’ and an ____ Gate for the carry.
0+0 = 00

0+1 = 01

1+0 = 01

1+1 = 10

Here the output ‘1’of ‘10’ becomes the carry-out. 
The result is shown in a truth-table below. ‘SUM’ 
is the normal output and ‘CARRY’ is the carry-out.

INPUTS                       OUTPUTS
============================================
 
A              B              SUM           CARRY
-------------------------------------------------

0              0              0              0

0              1              1              0

1              0              1              0

1              1              0              1

  OR

  NOT

  AND

  NOR

 4. In the half adder circuit below, what are the values for SUM and CARRY?
halfadder_1.png

  SUM = 0; CARRY = 1

  SUM and CARRY = 1

  SUM = 1; CARRY = 0

  SUM and CARRY = 0

 5. Half adders allow for complex addition, i.e cases when you have to add two 8-bit bytes together.

  TRUE

  FALSE

 6. A half adder circuit can add _______________and produce a digit bit (Q) and a carry bit.

  up to 8 billion bit numbers

  clock signals together with a single bit number

  two single bit numbers

  only 1s in a binary number

 7. A half adder specialises in dealing effectively with an incoming carry bit.

  FALSE

  TRUE

 8. One of the differences between a half adder and a full adder is that the full adder has three inputs and two outputs

  FALSE

  TRUE

 9. The half adder is a combination circuit of____________________ circuits. Its purpose, as the name suggests, is to add numbers

  AND and NAND

  XOR and AND

  OR and NOT

  OR and XOR

 10. It is possible, as shown in the diagram below, to construct a half adder using only NAND gates.
halfadder_2.png

  TRUE

  FALSE

 11. The half adder has two outputs, sum (S) and carry (C). The carry signal represents an _______into the next digit of a multi-digit addition

  oddity

  overflow

  exception

  OR gate

 12. In a half adder, the value of the sum is 2C + C + S.

  TRUE

  FALSE

 13. With the addition of an _____to combine their carry outputs, two half adders can be combined to make a full adder

  OR gate

  AND gate

  NOR gate

  NOT gate

 14. Can you spot the error in the following truth table for a half adder circuit?
Inputs	Outputs
A	B	C	S
-------------------------
0	0	1	0
1	0	0	1
0	1	0	1
1	1	1	0

  It is not possible to create a truth table for a half adder as it is not complete

  For the input A,B = 0,0, the 'Carry' output should be 0

  For the input A,B = 1,0, the SUM should be 0.

  There are no errors

 15. What is the following diagram showing?
halfadder_3.png

  Logic diagram for a half adder

  Logic diagram for two half adders connected to an 'AND' gate

  Logic diagram for several XOR, AND and OR gates - an adder has not been created in this example

  Logic diagram for a full adder