Digital Components - Adders Flashcards
What is the truth table for a half adder?
A B Cout Sum
0 0 0 0
0 1 0 0
1 0 0 0
1 1 1 1
What is Cout and sum in an adder?
When your values sum to 01, the C stands for Carry, the MSB, in this case 0 and the sum is 1.
Another example, use a half adder to sum A and B, A=1 B=1
Sum = 10
Cout = 1
Sum = 0
What is the Boolean expression for the Cout and Sum of a half adder?
Cout = AB
Sum = A ⊕ B
= A’B + AB’
What is the difference between a half adder and full adder?
The full adder will use an inputted carry for its final sum, unlike the half adder
What is the Boolean expression sum and Cin for a full adder?
Sum = (A ⊕ B) Cin
= (A’B + AB’) Cin
What is the Boolean expression for Cout of a full adder?
Cout = Cout from half adder + Cin
= AB + (A ⊕ B)Cin
What is the advantage of the parallel adder?
We can use it to add larger sums
Can we use a half adder anywhere in a Parallel adder?
No, the half adder can only be placed in the first adder position.
If we choose not to use a half adder and to use a full adder the whole way through, the first adder’s carry in should be connected to GND
See page 85
What is a group of 4 bits known as?
A nybble
What is a group of 8 bits known as?
A byte
What is cascading?
When we connect the Carry out of the previous adder (lower order) to the carry in of the next adder (higher order)
How can adders be used to count the number of yes or no votes?
- Each adder can sum up to the max number of votes programmed to do (e.g. two input adders (half adders) can only sum up to 2 votes at a time), so full adders would be better as they can sum 3 at a time with the Carry in.
- The adders are connected to a BCD 7 segment decoder which will convert these votes into a digital number on a screen
- If switches are used to say yes or no, then the neutral position of the switch ensures the resistors Ground the inputs of the adders.
- When the switch goes to a yes or no, the adder input is connected to the Vcc
