**Scenario:**

You work as a technical analyst for a large publisher of engineering text books. One of their well-known authors has set a number of further problems in her latest draft Digital Principles text, aimed at the level four engineering market. She wishes to set these further problems throughout the text and intends to provide the worked solutions on a companion website for the new book. The author has asked you to provide these worked solutions. The further problems are given in the following tasks: –

Activity:

**Tasks**

Consider the simple combinational logic circuit in Figure 1:

- Construct a Truth Table for the circuits Fig1, Fig 2 & Fig 3 .
- Construct a Karnaugh Map from your Truth Table.
- Use your Karnaugh Map to devise a simplified Boolean Algebra expression for the circuit.
- a) Numbering system
- Convert 3420
_{10}into Binary number system - Convert 1110101110
_{2}to the hexadecimal system. - Convert 4320
_{10}into the octal system. - Convert 01011010
_{2}to the hexadecimal system.

** Show all your working**

- b) . Given the following Boolean Algebra expression for a circuit:
- Construct a Truth Table for this circuit.
- Construct a Karnaugh Map from your Truth Table.
- Use your Karnaugh Map to devise a simplified Boolean Algebra expression for the circuit.

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