Selector

1
Selector

• A selector has two data inputs, and one output
• If S 1 then A appears on the output
• If S 0 then B appears on the output

2
Multiplexer

• A multiplexer connects multiple (2N) inputs to a
  single output
• Multiplexer chooses one specific input by using
  an additional set of N lines
• Multiplexers are used in digital circuits to
  control signal and data routing

3
4-to-1 Multiplexer implementation
4
Decoders

• In general a decoder has N inputs and 2N output
  lines.
• The outputs are numbered 0 to 2N-1
• Only one output line is asserted at a time
  depending on the input pattern

5
2 to 4 Decoder
6
Address decoding
Example 1k-byte memory using four 256x8-bit
memory RAM
7
Circuits for addition

• Designing a circuit to produce the sum of two
  binary digits P and Q.
• Both P and Q can be either 0 or 1
• The following facts are known
• 12 12 102
• 12 02 012
• 02 12 012
• 02 02 002
• The circuit must have 2 outputs
• one for the left binary digit (Carry)
• One for the right binary digit (Sum)

8
Half-Adder

• Carry output is 1 if both P and Q are 1
• The sum output is 1 if either P or Q, but not
  both, is 1
• Sum corresponds to the Boolean expression of XOR
• (P?Q) ??(P?Q)
• Carry can be produced using the AND gate (P?Q)

9
Full Adder

• To be able to construct a circuit that adds
  multidigit binary numbers, it is necessary to
  incorporate a circuit that will compute the sum
  of three binary digits (Full adder)
• Assume addition of three binary digits P, Q and R
• Add P and Q using a half adder to obtain a binary
  number with two digits
• P
• Q
• C1S1

10
Full Adder

• Add R to the sum C1S1 of P and Q
• C1S1
• R
• This is done by adding R to S1 using a half adder
  to obtain the two digit-number C2S
• S1
• R
• C2S
• Determine the left-most digit C of the entire sum
• C1 if C1 1 or C2 1

11
Full Adder
12
Addition

• Two full adders and one half adder can be used
  together to build a cicuit that will add two
  three digit numbers PQR and STU to obtain the sum
  WXYZ

13
Shifter

• Combinational circuits used to shift strings of
  0s and 1s one or more places to the left or right
• Typical 4 bit shifter operates as follows
• Example
• 1010
• Shift right 1
• Result 0101

14
Shifter
15
Memory

• Gates can be used to remember input
• Thus Gates can be used to build memory
• The Flip-flop is a bistable device, that exists
  in one of two states and, in the absence of input
  remains in that state

S-R Flip-flop or S-R latch
16
Flip-Flop

• The circuit has two inputs S (Set) and R (Reset)
  and two outputs Q and Q
• The S-R latch is defined with a characteristic
  table, which shows the next state or states of
  the circuit as a function of current states.

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Flip-Flop
18
Clocked S-R Flip-Flop

• Events in the digital computer are synchronized
  to a clock pulse
• Changes occur only when a clock pulse occurs

19
D Flip-Flop

• S-R flip-flop condition RS1 must be avoided
• D Flip-flop accomplishes this
• D Flip-flop is always equal to the most recent
  value applied to the input

20
Parallel Register