Use muxes to implement various gates. In each circuit, draw the specified number of 2:1 muxes and implement the given boolean expression. A mux input can be A, B, 0, 1, or the output of another device (e.g., another mux or a decoder). Be sure to label the S, 0, and 1 inputs of every mux. a. Use one 2:1 mux to implement NOT A (i.e. A') b.   Use two 2:1 muxes to implement A NAND B c.  Use one 2:4 decoder and one 2:1 mux to implement A XOR B

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Use muxes to implement various gates. In each circuit, draw the specified number of 2:1 muxes and implement the given boolean expression. A mux input can be A, B, 0, 1, or the output of another device (e.g., another mux or a decoder). Be sure to label the S, 0, and 1 inputs of every mux.

a. Use one 2:1 mux to implement NOT A (i.e. A')

b.   Use two 2:1 muxes to implement A NAND B

c.  Use one 2:4 decoder and one 2:1 mux to implement A XOR B Note that the 2-bit values on the right are arranged as B1 B0 (that is, the bottom wire corresponds to the first, not the second, bit).

### Understanding a 2:4 Decoder

#### Diagram Explanation:
The image illustrates a 2:4 decoder. This is a digital logic component used to convert 2-bit binary inputs into 4 distinct outputs. 

#### Components:
- **Inputs:** 
  - \( B_0 \)
  - \( B_1 \)
  
- **Outputs:** 
  - 00
  - 01
  - 10
  - 11

#### Functionality:
A 2:4 decoder takes two binary inputs and decodes them into four unique outputs. Each output corresponds to one of the binary combinations of the inputs:

- Input \( B_0B_1 = 00 \) activates the first output.
- Input \( B_0B_1 = 01 \) activates the second output.
- Input \( B_0B_1 = 10 \) activates the third output.
- Input \( B_0B_1 = 11 \) activates the fourth output.

This type of decoder is commonly used in digital systems for decoding instructions, address decoding in microprocessors, and similar applications where binary input needs to be translated into a specific output line.
Transcribed Image Text:### Understanding a 2:4 Decoder #### Diagram Explanation: The image illustrates a 2:4 decoder. This is a digital logic component used to convert 2-bit binary inputs into 4 distinct outputs. #### Components: - **Inputs:** - \( B_0 \) - \( B_1 \) - **Outputs:** - 00 - 01 - 10 - 11 #### Functionality: A 2:4 decoder takes two binary inputs and decodes them into four unique outputs. Each output corresponds to one of the binary combinations of the inputs: - Input \( B_0B_1 = 00 \) activates the first output. - Input \( B_0B_1 = 01 \) activates the second output. - Input \( B_0B_1 = 10 \) activates the third output. - Input \( B_0B_1 = 11 \) activates the fourth output. This type of decoder is commonly used in digital systems for decoding instructions, address decoding in microprocessors, and similar applications where binary input needs to be translated into a specific output line.
Expert Solution
Step 1: State the given data.

We need to draw the following,

a. Use one 2:1 mux to implement NOT A (i.e. A')

b.   Use two 2:1 muxes to implement A NAND B

c.  Use one 2:4 decoder and one 2:1 mux to implement A XOR B Note that the 2-bit values on the right are arranged as B1 B0 (that is, the bottom wire corresponds to the first, not the second, bit).

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