I am new at digital design and I have a problem. I need to get the number of zeros. There must be 4 inputs and I must use only half-adders. I tried everything I know but I could not solve this. Do you have an idea?
Answer
Phase 1, invert all inputs.
- That way we can identify zeros as logic 1. and Logic 1 can be quantified easily with a half adder as oppose to logic 0.
Phase 2, Combine half-adders to make a 4-bit adder.
- Half-Adder can add 2-bits
- Full-Adder can add 3-bits
- Hald-Adders + Full-Adders + Ripple Carry can add n-bits
What Half Adder and Full Adder look like
How to build an inverter with a half-adder:
- keep one of the exclusive-or inputs high. Then the exclusive-or gate acts like an inverter
simulate this circuit – Schematic created using CircuitLab
NOT gate using a single Half-Adder
How to build an or gate with only half-adders, in case you need it to build the full-adder and n-bit adder:
First, build a nand gate using a half adder. Second, build an or gate from nand gates.
- You can do it by attaching the input of the not gate to the and gate.
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