Logic Gates

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    \node[left of=and1, xshift=-1cm] {AND};
    \node[left of=or1, xshift=-1cm] {OR};
    \node[left of=not1, xshift=-1cm] {NOT};
    \node[left of=nand1, xshift=-1cm] {NAND};
    \node[left of=nor1, xshift=-1cm] {NOR};
    \node[left of=xor1, xshift=-1cm] {XOR};
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• A logic function (or Boolean function) is a function that takes one or more bits of input and produces a single bit of output.

• A logic gate (or simply gate) is a device that implements a logic function.

• Multiplexors

  • selector (or control) value
  • B.3 Combinational Logic B-11 — Two-Level Logic and PLAs

• logic circuits

  • a combinational logic (מעגל צירופי) is a device consisting of logic gates whose outputs at any time are determined by the current inputs
  • a sequential logic (מעגל סדרתי) is a device consisting of logic gates whose outputs at any time are determined by the current inputs and the previous state of the device

• packaged building-block logic families can be divided into categories:

  • resistor-transistor logic (RTL) circuits are logic circuits built from resistors and transistors
  • diode-transistor logic (DTL)
  • transistor-transistor logic (TTL)

• An integrated circuit (IC) is a device that contains many logic gates on a single chip of silicon

  • ICs have external electrical contact points called pins
  • A package is a plastic or ceramic case that holds the IC and connects the pins to the outside world
  • A dual in-line package (DIP) is a package with two parallel rows of pins

• A discrete component is an electronic device containing only a single element, such as a transistor or a resistor

Arithmetic logic circuits

Binary adders

Half Adder

• A half adder addes two single binary digits $A$ and $B$, and outputs a sum bit $S$ and a carry out bit $C_{\text{out}}$
  • The sum bit ($S$) is a XOR of $A$ and $B$
  • The carry out bit ($C_{\text{out}}$) is an AND of $A$ and $B$
  • The carry out bit represents an overflow into the next digit of a multi-digit addition

$A$	$B$	$S$	$C_{\text{out}}$
0	0	0	0
0	1	1	0
1	0	1	0
1	1	0	1

Full Adder

• A full adder adds two bits $A$ and $B$ and accounts for values carried in as well as out, and outputs a sum bit $S$ and a carry out bit $C_{\text{out}}$
  • $S=A\oplus B\oplus C_{\text{in}}$
  • $C_{\text{out}}=(A\cdot B)+(C_{\text{in}}\cdot (A\oplus B))$

$A$	$B$	$C_{\text{in}}$	$S$	$C_{\text{out}}$
0	0	0	0	0
0	0	1	1	0
0	1	0	1	0
0	1	1	0	1
1	0	0	1	0
1	0	1	0	1
1	1	0	0	1
1	1	1	1	1

Sequential Logic

• SR latch (Set-Reset latch) is a simple form of sequential logic that can store one bit of information
• flip-flop
  • JK flip-flop

Boolean Algebra

Logic Gate
OR	$A+B$	logical sum
AND	$A\cdot B$	logical product
NOT	$\overline{A}$

Laws

• Identity law: $A+0=A$, $A\cdot 1=A$
• Zero and one law: $A+1=1$, $A\cdot 0=0$
• Inverse law: $A+\overline{A}=1$, $A\cdot \overline{A}=0$
• Commutative law: $A+B=B+A$, $A\cdot B=B\cdot A$
• Associative law: $(A+B)+C=A+(B+C)$, $(A\cdot B)\cdot C=A\cdot (B\cdot C)$
• Distributive law: $A\cdot (B+C)=A\cdot B+A\cdot C$, $A+(B\cdot C)=(A+B)\cdot (A+C)$