ECE 275: Adders

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\[ \newcommand{\bx}{\bar{x}} \newcommand{\by}{\bar{y}} \newcommand{\bz}{\bar{z}} \newcommand{\bA}{\bar{A}} \newcommand{\bB}{\bar{B}} \newcommand{\bC}{\bar{C}} \newcommand{\bD}{\bar{D}} \newcommand{\bE}{\bar{E}} \]

Announcments

  • Homework 5 is due on Oct 15th, 9 AM before class.
  • Read 3.1 to 3.33 of textbook by Wednesday.

Half adder

Design a Multi-output circuit that adds two 1-bit binary numbers \(x_0\) and \(y_0\) and outputs a sum \( s_0 \) and carry bit \( c_1 \).
\( x_0 \)\( y_0 \)\( s_0 \)\( c_1 \)
0 0 0 0
0 1 1 0
1 0 1 0
1 1 0 1

Half Adder

Full adder

Design a Multi-output circuit that adds three 1-bit binary numbers \(x_i\), \(y_i\) and \(c_{i}\) outputs a sum \( s_i \) and carry bit \(c_{i+1} \).
\( c_i \) \( x_i \)\( y_i \)\( s_i \)\( c_{i+1} \)
0 0 0 0 0
0 0 1 1 0
0 1 0 1 0
0 1 1 0 1
1 0 0 1 0
1 0 1 0 1
1 1 0 0 1
1 1 1 1 1

Full adder

Brown and Vranesic (2014)

Decomposed Full adder

Design a Full adder in terms of two Half Adders

Decomposed Full adder

Brown and Vranesic (2014)

Ripple carry adder

Design a 4-bit adder using 4 Full adders

Ripple carry adder

Brown and Vranesic (2014)

More circuit symbols

Multiplexer

Adder

More circuit symbols

Multiplexer

Adder

Design a 4-bit Adder/Substractor unit

Using an adder and 1's complement unit.

Adder/Substractor unit

Gray code

Binary coded Decimal

Thanks, Questions, Feedback?

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