Basic Adders-Digital Electronics, Slides of Digital Electronics

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EEE130 Digital Electronics I

Lecture

• Functions of Combinational Logic -

By Dr. Shahrel A. Suandi

Topics to be covered

• 6-1 Basic Adders

• 6-2 Parallel Binary Adders

• 6-3 Ripple Carry versus Look-Ahead Carry Adders

• 6-4 Comparators

• 6-5 Decoders

• 6-6 Encoders

• 6-7 Code Converters

• 6-8 Multiplexers (Data Selectors)

• 6-9 Demultiplexers

• 6-10 Parity Generator/Checkers

Symbols used for adders

A B Cout  0 0 0 0 0 1 0 1 1 0 0 1 1 1 1 0

Half-adder Full-adder

A B Cin Cout  0 0 0 0 0 0 0 1 0 1 0 1 0 0 1 0 1 1 1 0 1 0 0 0 1 1 0 1 1 0 1 1 0 1 0 1 1 1 1 1

6-2 Parallel Binary Adders

• More than two full-adders can be connected to form

parallel binary adders

• How they are arranged?

• Parallel/cascade by connecting from the lower bit to in a higher bit

• Why they are needed?

• To add binary numbers more than 2 bits; ie. For 2-bit numbers, 2 adders are needed; 4-bit numbers, 4 adders are needed, and so on

• What important things that we should remember?

• A full adder can be used instead of half adder – the LSB concerned full adder must be connected to ground
• Let’s see everything graphically…

74LS283 4-bit parallel adder

Adder expansion

Ripple carry adder

• A ripple carry adder is one in which the carry output of

each full-adder is connected to the carry input of the

next higher-order stage

• Why delayed/slow?

• The sum and the output carry of any stage cannot be produced until the input carry occurs

Look-ahead carry adder

• The look-ahead carry adder anticipates the

output carry of each stage, and based on the

inputs, produces the output carry by either

carry generation or carry propagation

A 4-bit Comparator (74HC85)

How to connect two 74HS85s

A 1-of-16 Decoder (74HC154)

6-6 Encoders

• An encoder is a combinational logic circuit

that essentially performs a “reverse”

decoder function

• Tips to remember when to use encoders

– Decimal/octal  BCD or binary

6-8 Multiplexers

• A multiplexer (MUX) is a device that allows

digital information from several sources to

be routed onto a single line for

transmission over that line to a common

destination

• Also known as “data selector”

A1-of-4 data

selector/multiplexer ()