digital logic - Counting the number of 0's

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

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What Half Adder and Full Adder look like

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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

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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.

^{simulate this circuit}

NAND gate using 2 half-adders

OR gate using 3 NANDs