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Engineering the Future. Electrical Engineering. Digital Circuits Fundamentals Hands-on Full-Adder Simulation (afternoon). Engineering the Future. Electrical Engineering:. Digital Circuits Fundamentals Binary Numbers Binary Functions. Decimal Numbers. Binary Numbers. Binary Numbers.

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electrical engineering

Engineering the Future

Electrical Engineering

Digital Circuits FundamentalsHands-on Full-Adder Simulation

(afternoon)

electrical engineering1

Engineering the Future

Electrical Engineering:

Digital Circuits Fundamentals

Binary Numbers

Binary Functions

binary counting exercise
Binary Counting Exercise
  • Count up to ? Using 2 bits
  • Count up to ? Using 3 bits
  • Count up to ? Using 4 bits
  • Count up to ? Using 5 bits
  • Count up to ? Using 6 bits
logic gates3
Logic Gates

http://www.williamson-labs.com/480_logic.htm#doors

binary addition networks half adder
Binary Addition Networks (Half Adder)

With two’s complement numbers, addition is sufficient

SUM

Half-adder Schematic

CARRY

binary addition networks cascaded multi bit adder
Binary Addition Networks (Cascaded Multi-bit Adder)

usually interested in adding more than two bits

this motivates the need for the full adder

binary addition networks full adder
Binary Addition Networks (Full Adder)

S = A’B’CI+A’BCI+AB’CI’+ABCI = CI xor A xor B

CO = B CI + A CI + A B = CI (A + B) + A B

one bit adder

A

S

B

Cout

Cin

A B Cin S Cout

0 0 0 0 0 1

0 1 0

0 1 1

1 0 0 1 0 1

1 1 0

1 1 1

0

1

1

0

1

0

0

1

0

0

0

1

0

1

1

1

One-bit adder
  • 1-bit binary adder
    • inputs: A, B, Carry-in
    • outputs: Sum, Carry-out
binary addition networks full adder half adder
Binary Addition Networks (Full Adder/ Half Adder)

Standard Approach: 6 Gates

Alternative Implementation: 5 Gates

SUM

CARRY OUT

CARRY IN

CO = A B + CI (A xor B) = A B + B CI + A CI