1. According to the circuit diagram, derive it step by step to obtain the final output logical function expression.

2. Based on the output function expression, list the truth table

3. Based on the truth table, summarize the basic functions of logical functions

One-bit full adder (completes the addition of one-bit binary numbers, 3 inputs, 2 outputs)

Serial carry adder (conforms to the rules of arithmetic operations, input and output are from low to high)

Carry-lookahead adder (carry signals for each bit are generated in parallel)

The output binary number reflects the input situation [N (input) <= 2**n (output)] (more end to less end)

Simple encoder (cannot recognize the priority of the input signal)

priority encoder

Function extension

Translate the input binary number and output it (N output <= 2**n input) (Yi=mi)

2-wire to 4-wire decoder (truth table, logic symbols)

3-wire to 8-wire decoder

4-line to 10-line decoder (BCD-decimal decoder) (if A3 is regarded as an active low-level enable terminal, it can be regarded as a 3-line to 8-line decoder)

Function expansion (the newly added input terminal is generally used as a high-order input terminal to enable the output terminals to be arranged in an orderly manner)

To change the enable input, you can use the decoder as a data distributor (one to many) (distribute the enable input to different outputs according to different address variables)

Seven-segment display decoder

One bit numerical comparator

Integrated four-digit numerical comparator

Bit extension (from high bit ratio to low bit ratio)

N input terminal=2**n address terminal, (Y=åmiDi)

4-to-1 data selector

Dual 4-to-1 data selector

8-to-1 data selector

Function extension