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Binary Addition

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The Half-Adder and Exclusive OR Gate. Exclusive OR. Typically abbreviated to XOR ... A full adder is a circuit with three inputs (including a carry-in') and two ... – PowerPoint PPT presentation

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Title: Binary Addition


1
Binary Addition
  • CSC 103
  • September 17, 2007

2
Recap Binary Numbers
  • Physical representation
  • Transistor
  • Concept of on and off for physical
    manufacturing of computers ? T/F
  • Abstract representation
  • Logic NOT, AND, OR
  • Truth tables
  • ANY Boolean expression can be built with
    transistors wired as AND, OR or NOT

3
Recap Transistors
0
1
0 or 1
1 or 0
1
4
Logic Functions NOT
  • The NOT function
  • A A
  • 0 1
  • 1 0

5
Recap Logic Gate AND Function
(1)
1
(1)
0
0
0
1
0
0
6
Logic Gate OR Function
1
0
1
1
0
1
0
7
  • Onto Addition and
  • the Adder Circuit...

8
Binary Addition
  • Add
  • 0 0
  • 0 1
  • 1 0
  • 1 1
  • Add these numbers
  • c
  • 1000111 1011010
  • 0100110 0111001
  • s

9
Binary Addition Half Adder
  • We need a circuit to add two bits
  • Either bit can be 0 or 1
  • The function in the truth table is
  • Sum AB AB ? Exclusive-OR function
  • Carry AB

10
The Half-Adder and Exclusive OR Gate
  • AB AB Exclusive OR
  • Typically abbreviated to XOR
  • Simulator uses EOR

A B A B A B
A B
A B S C 0 0 0 0 0 1
1 0 1 0 1 0 1 1
0 1
11
Recap Logic Gates Symbols
AB, A?B AB
A, A
XOR
12
Summary The Half-Adder and Exclusive OR Gate
  • Exclusive OR
  • Typically abbreviated to XOR
  • Simulator uses EOR

A B
13
Binary Addition Half Adder
14
Half-Adder ? Full-Adder
15
The Full Adder
  • A full adder is a circuit with three inputs
    (including a carry-in) and two outputs (the sum
    and carry-out)
  • What is the third input?
  • Exercise Add 111 101
  • (carry)
  • 1 1 1 ( A )
  • 1 0 1 ( B )
  • (sum)
  • For adding two numbers, we need three inputs

16
The Full Adder
  • Cascade two half-adders to get a full adder

A B Cin
17
HW Cascade 2 Full Adders for a 2-Bit Adder
A2A1 ? 1 1 B2B1 ?
1 0
B2 A2 B1 A1
Full Adder
Full Adder
Cout2 Cin2 Cout1
Cin1
S2 S1
18
Summary
  • Binary addition
  • Concept of sum and carry
  • Half adder and full adder circuits
  • Cascading circuits to make larger ones
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