CSC258H1 Lecture Notes - Multiplexer, Binary Number

34 views1 pages
Published on 20 Apr 2013
School
UTSG
Department
Computer Science
Course
CSC258H1
Professor
Page:
of 1
LOGIC DEVICES
Building up from gates
o Some common and more complex structures
Multiplexers (MUX)
Adders (half and full)
Subtractors
Comparators
Decoders
Seven-segment decoders
o Certain structures are common to many circuits, and have block
elements of their own
Karnaught map review moved to jan18ce
Multiplexers (MUX)
o Behavior:
output is X if S = 0; otherwise output is Y if S = 1
o Multiplexer design
X
Y
S
M
M
 
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
1
1
1
0
0
1
    
1
0
1
0
1
1
0
1
1
1
1
1
Adders
o Also known as binary adders
Small circuits devices that add two digits together
Combind together to create interative combinational circuits
o Types of adders
Half Adders (HA)
Like an OXR for sum (s) and AND for carry (c)
Full Adders (FA)
Ripple Carry Adder
Carry-Look-Ahead Adder (CLA)
o Binary Math review
Each digit of a demical number represents a power of 10:
258 = 2*102 + 5*101 x+ 8*100
Each digit of a binary number represents a power of 2:
011012 = 0*24 + 1*23 + 1*22 + 0*21 + 1*20
= 1310
Binary Addition example
27 + 53 95 + 181
27 = 00011011 95 = 01011111
53 = 00110101 181 = 10110101
o Half Adders
A 2-input, 1-bit width binary adder that performs the following
computations:
A half adder adds two bits to produce a two-bit sum
The sum is expressed as a sum bit S and a carry bit C
Half Adder Implementation
Equations and circuits for half adder units are easy to
define (even w/o k-maps)
      
o Full Adders
Similar to half-adders, but with another input Z, which
represents a carry-in bit
C and Z are sometimes labels as Cout and Cin
When Z is 0, the unit behaves exactly like a half adder
When Z is 1, the full adder performs the following computations
Full Adder Design
X
Y
S
C
C
 
 
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
1
1
1
S
 
 
1
0
0
0
0
1
0
1
1
0
1
1
1
0
1
0
1
1
0
1
1
1
1
1
         
      
  
Then let carry generate  
And let carry propagate   
Resultant circuit
o Ripple-Carry Binary Adder
Full adder units chained together in order to perform operations
on singal vectors
o The role of Cin
Why can’t we judt have a half-adder for the smallest (right-
most) bit?
We could, if we were only interested in addition. But the last bit
allows use to do subtraction as well.

Document Summary

Building up from gates: half adders. A 2-input, 1-bit width binary adder that performs the following: some common and more complex structures computations: Seven-segment decoders: certain structures are common to many circuits, and have block elements of their own. Karnaught map review moved to jan18ce. Output is x if s = 0; otherwise output is y if s = 1. A half adder adds two bits to produce a two-bit sum. The sum is expressed as a sum bit s and a carry bit c. Equations and circuits for half adder units are easy to define (even w/o k-maps: full adders. Similar to half-adders, but with another input z, which. C and z are sometimes labels as cout and cin. When z is 0, the unit behaves exactly like a half adder. When z is 1, the full adder performs the following computations: multiplexer design. Adders: also known as binary adders. Small circuits devices that add two digits together.