Power Point Presentation

1
Power Point Presentation

• Donald Bearden
• CS 147
• September 13, 2001

2
Topics Covered

• Sec 1.3.5 Adders and Subtractors
• Sec 1.3.6 Memory
• Sec 1.4.1 BCD to 7-segment Decoder
• Sec 1.4.2 Data Sorters

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1.3.5 Adders and Subtractors

• The circuits used to perform arithmetic
  operations are constructed using combinatorial
  logic. ADDERS are the most commonly used.
• HALF ADDERS are the most basic of the adders. It
  inputs two 1-bit values, X and Y and outputs
  their 2-bit sum as bits C(carry) and S(sum).

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A half adder

• Truth table
• X Y C S
• -------------
• 0 0 0 0
• 0 1 0 1
• 1 0 0 1
• 1 1 1 0

Half adder
Y
X
S
C
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1.3.5 Adders and Subtractors

• FULL ADDER was developed to add numbers that are
  more than one bit wide. It has three inputs the
  two data inputs and a carry input(Cin). The
  output is the same as the half adder.

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FULL ADDER

• Truth table
• X Y Cin C S
• -------------------
• 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 1 1 0
• 1 1 1 1 1

X
Y
Full adder
Cin
C
S
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1.3.5 Adders and Subtractors

• RIPPLE ADDER full adders cascaded to produce an
  n-bit adder by connecting output C of an adder to
  Cin of th enext adder. The reason its called a
  ripple adder is the carry bits ripple through the
  adder.
• Each full adder has a small PROPAGATION DELAY,
  which adds up as the carry bits are propagated,
  or ripple, from right to left.
• One solution to the delay problem is the CARRY
  LOOKAHEAD ADDER. This adder breaks the
  implementation of the carry into two parts the
  GENERATE, g part and the PROPAGATE, p.

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1.3.5 Adders and Subtractors

• FULL SUBTRACTORS are logic components that
  directly subtract two values. It has three
  inputs two data inputs and a borrow input.
• TWOs COMPLEMENT can also be used to implement
  subtraction. Twos complement of a value is the
  negative of that value. It is generated by
  complementing the value and adding 1.

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1.3.6 MEMORY

• MEMORY is a group of circuits used to store data.
  Although not strictly combinatorial in design, it
  can be used as combinatorial components in
  digital circuits.
• A memory component has some number of memory
  locations, each of which stores a binary value of
  some fixed length.
• The number of locations and the size of each
  location vary from memory chip to memory chip,
  but are fixed within an individual chip.
• The size of the chip is denoted as the number of
  locations times the number of bits in each
  location. A memory chip of size 512 x 8 has 512
  memory.
• A memory chip with 2(n) locations requires n
  ADDRESS inputs.,
• The DATA pins on a memory chip are used to access
  the data.

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1.3.6 Memory

• The two primary classes of chips are ROM(Read
  only memory) and RAM(Random access memory).
• Data is programmed into the ROM chip using a
  separate ROM programmer. The circuit does not
  change the contents of the ROM.
• PCs use ROM to store the instructions that
  constitute their BIOS(Basic input/output
  system).When power is removed from a ROM chip, it
  still maintains its data. ROM is nonvolatile.
• RAM is often referred to as read/write memory.
  Unlike ROM, it initially contains no data. Data
  can flow in to or out of the chip, as opposed to
  ROM, which are output only. RAM loses its data
  once power is removed it is volatile.

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Combinatorial Circuit Designs

• Many circuits can be designed using gates and
  components. Two of these designs are BINARY
  CODED DECIMAL(BCD) to 7-segment decode and a
  simple DATA SORTER.

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1.4.1 BCD to 7-segment Decoder

• BCD(Binary coded decimal) to 7-segment decoder is
  used in digital displays.It converts the binary
  representation of a decimal digit, 0000 to 1001
  to the signals needed to show the digit on a
  7-segment LED display.
• This circuit is actually seven distinct circuits,
  one for each segment, a through g. The design
  process for each is the same. For many
  applications, it is preferable to use ACTIVE LOW
  display-that is, a 0 lights the display and a 1
  blanks the display.

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7-Segment LED display
Patterns
a
0 1 2 3 4 5 6 7 8 9
Segment labels
f
b
g
e
c
d
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1.4.2 Data Sorter

• A simple DATA SORTER will input a 4-bit values
  and output them in descending order. The basic
  building block of this circuit is the
  compare-and-swap modules. It receives two data
  inputs and compares them using the 4-bit
  comparator.

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Four-input data sorter
a b
X
max
X Y
max
Y
min
min
max
X Y
min
C d
max
max
X Y
X Y
min
min