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example sum (using more than 1 bit):
1 0 1 0 0 1
Why not convert to decimal to check all this really works?
We leave it as an exercise for you to complete the table.
You will probably also want to draw the Karnaugh Maps for the Sum and Carry out circuits.
Then you could go on to design the full adder although this is a circuit well outside the expected range for this course.
What would a full-adder circuit look like when expanded to show all logic gates? Draw it using XOR, OR and AND gates.
For these exercises, construct the truth table , derive the expression (minterms), minimise if possible, using algebra and/or K-maps.
Recall that binary addition has the following rules for the addition of two binary digits, A and B:
Following on from the previous page, you should be able to see that the Sum is A XOR B whereas the Carry is A and B, expressed as Boolean algebra:
Sum = A and B
Carry = A xor B
The half-adder circuit with one XOR and one AND gate is shown.
When adding binary numbers that have more than 1 bit, the carry must be added to the next column on the left, a full-adder has a truth table like the following:.
A full adder is constructed from 2 half adders with the carry from each half adder going to an OR gate. Schematically:
The following schematic circuit is a 2-to-1 line multiplexer, if C is 0 then -Y=A else Y=B:
1. Draw the truth table and derive the algebraic expression for the circuit. Construct the circuit using appropriate gates.
2. Design a circuit that compares three inputs A, B and C and whose output Y is a one if all inputs are equal.
3. Design a circuit that compares the same three inputs as above but outputs a one if any two out of the three inputs are a 1.
3. Design a circuit that compares the same three inputs as above but outputs a one if an odd number of 1's is input. What could this circuit be used for? Have you seen it before?
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This page was last modified: October 28, 2013