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Half Adders

A half adder is designed to combine two binary digits and produce a carry. So, it has two inputs bits and can generate a sum bit plus a carry. So there should be two bits of output.

• Data inputs: 2 (call them x and y)
• Outputs: 2 (call them s, for sum, and c, for carry)

Truth table and two logic blocks for HA:

c=xy

S=xy

Full Adders:

Full adder becomes necessary when a carry input must be added to the two binary digits to obtain the correct sum. A half adder has no input for carries from previous circuits.

Characteristics of FA:

• Data inputs: 3 (call them x, y, and c_in, for carry in)
• Outputs: 2 (call them s, for sum, and c_out, for carry out)

Truth table and two logic blocks for FA:

Number Systems

    - Conventional Number System

         >Properties

         >Binary, Decimal, Hexadecimal

         >Number Base Conversion

    - Unconventional Number System

         >Roman Number System

         >Signed Digit Number System

         >Binary SD Number System

Fast Addition

    - Half and Full Adders

    - Ripple Carry Adder

    - Carry Look-Ahead Adders

Fast Multiplication

    - Carry Save Adders

    - Additive & Non-additive Multiplier

    - Counters