1
2
A
decimal number such as 7392 represents
7392.34 = 7x103 + 3x102 + 9x101 + 2x100+3x10-1+4x10-2
It
is practical to write only coefficients and deduce power of 10s from position
In general, any radix (base) can be used
Define
coefficients ai in radix
ECE 223 Digital Circuits and Systems
Boolean Algebra & Logic Gates
1
Binary (Boolean) Logic
Deals
Has
with binary variables and binary logic functions
two discrete values
0 False, Open 1 True, Close
Three
basic logical operations
AND (.); OR (+); NOT (
ECE 223 Digital Circuits and Systems
Logic Minimization
1
Karnaugh Maps - Introduction
2-Level Logic implementation using SOP or POS is not the most economical in terms of #gates & #inputs A Karnaugh map is a graphical representation of a truth table
The
ECE 223 Digital Circuits and Systems
Combinational Logic
1
Combinational Circuits
consists of logic gates with outputs that are determined entirely by the present value of the inputs (no memory)
Combinatorial circuits might be 2-level logic (SOP,POS) or m
ECE 223 Digital Circuits and Systems
Synchronous Logic
1
Sequential Circuits
Combinational circuits
Output = f (present inputs)
Sequential circuits
Output = f (present inputs and past inputs) Circuit remembers past history Must contain memory
inputs k com
Sequential Circuits
Have considered only combinational circuits in which circuit outputs are determined entirely by current circuit inputs. We can include storage elements into a circuit that act like memory and store a system state.
inputs
combinatorial
ECE 223 Digital Circuits and Systems
Registers & Counters
1
Registers
Register is a group of flip-flops
n-bit register has n flip-flops Can hold n bits of binary data Register may also contain combinational logic
2
Register with Parallel Load
Specific con
Registers
A single flip-flop stores one bit of information. A collection of n flip-flops stores n bits of information these flip-flops form what is called an n-bit register.
E&CE 223 Digital Circuits and Systems
Page 1
Registers
Illustration of a 4-bit re
Chapter 7
Memory and
Programmable Logic Devices
Memory
Random Access Memory (RAM)
Contrary to Serial Access Memory (e.g. Tape)
Static Random Access Memory (SRAM)
Data stored so long as Vdd is applied
6-transistors per cell
Faster
Differential
Dynamic