CHAPTER 2 : DIGITAL LOGIC

LOGIC DESIGN

• Digital electronics operate with only two voltage levels

         * high voltage and low voltage

• Computer used binary system (0,1).

• Combinational logic block contains no memory.

• Logic block with n inputs, there are 2n entries (possibility) in the truth table.

TRUTH TABLES

BOOLEAN ALGEBRA

• Boolean algebra laws

GATES

• Logic blocks are built from gates that implement basic logic functions.
• Any logical function can be constructed using AND gates, OR gates, and inversion.
• Two common inverting gates are called NOR and NAND.

DECODER

• Use decoder to build larger components.
• The most common type of decoder has an n-bit input and 2n-bit outputs, where only one output is asserted for each input combination.
• This decoder translates the n-bit input into a signal that corresponds to the binary value of the n-bit input.
• The outputs are shows a 3-bit decoder and the truth table. This decoder is called a 3-to-8 decoder.
• Since there are 3 inputs and 8 (2 power of 3) outputs. There is also a logic element called an encoder that performs the inverse function of a decoder, taking n inputs and producing an n-bit output.

MULTIPLEXER (Selector)

• The output is one of the inputs that is selected by a control.

• Multiplexers can be created with an arbitrary number of data inputs.
• If there are only two inputs, the selector is a single signal that selects one of the inputs.
• If it is true (1) and the other if it is false (0). If there are n data inputs, there will need to be [log2n] selector inputs.
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  To associate the inputs with selector values, we often label the data inputs numerically.

ARITHMETIC LOGIC UNIT (ALU)

• ALU – perform arithmetic operation (addition, subtraction and logical operation : AND, OR).
• Constructs an ALU from four hardware building blocks (AND and OR gates, inverters, and multiplexors) and illustrates how combinational logic works.
• MIPS word is 32 bits wide, so need 32-bit-wide ALU (connect 32 1-bit ALUs ).

1-Bit ALU

This adder is called a full adder; it is also called a (3,2) adder because it has 3 inputs and 2 outputs. An adder with only the a and b inputs is called a (2,2) adder or half-adder.

Specify the outputs of this "black box" based on its inputs, as in truth tables.

References:

Source 1
Source 2
Source 3