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Binary Math Circuits
11 questions By Tony R. Kuphaldt
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Question 4 of 11
Design a circuit that adds two binary bits together. This circuit will have two inputs (A and B) and two outputs (Sum and Carry):
Begin the design process by drawing a truth table for the circuit, then determining the necessary gate circuitry to fulfill each output function.
Why is this circuit referred to as a half adder? How would a full adder circuit differ from this?
Reveal answer
Notes:Have your students explain their design process to you, step by step. This circuit diagram is easy enough to discover in the pages of a textbook, so don’t be surprised if students simply copy what they see without trying to understand how it works!
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Question 5 of 11
Design a circuit that adds two binary bits and a “Carry in” (Cin) bit together, producing a “Sum” (Σ) and a “Carry out” (Cout) output:
Begin the design process by drawing a truth table for the circuit, writing a boolean SOP expression for each output, then determining the necessary gate circuitry to fulfill each output function.
Reveal answerΣ = ABC + AB C+ A BC+ ABC Cout = ABC + A BC + AB C+ ABC 
Notes:Have your students explain their design process to you, step by step. This circuit diagram is easy enough to discover in the pages of a textbook, so don’t be surprised if students simply copy what they see without trying to understand how it works!
Deriving the two cascaded Ex-OR gates from the boolean expression is a bit tricky, but not impossible. Remind your students if necessary that the boolean equivalent for the Ex-OR function is [A]B A, and that the Ex-NOR function is AB [A] .
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Question 6 of 11
Explain the difference between a ripple adder and a look-ahead adder. What does the term “ripple” mean in this context? Why is “ripple” potentially a bad thing for a digital adder circuit?
Reveal answer“Ripple” adders update their output bits one at a time rather than simultaneously. This leads to false, transient output states.
Notes:The “ripple” effect seen in simple binary adder circuits is not limited to adders! Some Gray-to-binary code converters and counter circuits also exhibit ripple, with the same deleterious effects.
