EE1A2 Microprocessor Systems

1
EE1A2Microprocessor Systems Digital Logic

• Part A
• Digital Electronic System Design
• Written by Dr. Tim Collins
• Edited and presented by Dr Sandra I. Woolley

2
Content

• Binary Arithmetic
• Addition and subtraction.
• Arithmetic circuits.
• Arithmetic Logic Units
• Microcontrollers
• Microcontroller architecture.
• Essential building blocks of a computer.
• Programming

3
Binary Arithmetic

• Number Systems
• Decimal
• Binary
• Hexadecimal
• Addition
• Long addition
• Full adder circuits
• Parallel adders
• Carry-look-ahead circuitry
• Subtraction
• Twos complement
• Subtraction using a parallel adder

4
Arithmetic Logic Units

• Adder-Subtraction Circuit
• Combining addition and subtraction in a single
  controllable circuit
• Arithmetic Logic Units
• General-purpose arithmetic and logic
  calculation units
• Registers
• How memory circuits can simplify the connections
  to an ALU

5
The Anatomy of a Microcontroller

• Tri-State Ports and Busses
• How a bus can interconnect many different
  registers without huge wiring difficulties.
• Connecting an ALU to a Bus
• The Building Blocks of a Computer
• ALU
• Registers
• I/O Ports
• Program Memory
• Programs

6
Number Systems Decimal

• Base 10
• Ten digits, 0-9
• Columns represent (from right to left) units,
  tens, hundreds etc.

7
Bases

• When counting upwards in base-10, we increase the
  units digit until we get to 10 when we reset the
  units to zero and increase the tens digit.
• So, in base-n, we increase the units until we get
  to n when we reset the units to zero and increase
  the ns digit.
• Consider hours-minutes-seconds as an example of a
  base-60 number system

Eg. 125843 000320 130203

• NB. The base of a number is often indicated by a
  subscript. E.g. (123)10 indicates the base-10
  number 123.

8
Binary

• Base 2
• Two digits, 0 1
• Columns represent (from right to left) units,
  twos, fours, eights etc.

9
Binary Numbers Terminology

• Each digit in a binary number is known as a
  bit.
• A group of eight bits makes a binary number known
  as a byte.
• A group of more than eight bits is known as a
  word.
• Typical word lengths 12, 16, 32, 64.

http//www.thinkgeek.com/tshirts/frustrations/5aa9
/
10
Decimal to Binary Conversion
Example Converting (123)10 into binary
123 2 61 remainder 1 61 2 30 remainder
1 30 2 15 remainder 0 15 2 7 remainder
1 7 2 3 remainder 1 3 2 1 remainder
1 1 2 0 remainder 1
11
Twos Complement

• One byte (eight bits) can be used to represent
  the decimal number range
• 0 to 255 (unsigned)
• -128 to 127 (signed)
• Negative binary numbers are formed by subtracting
  from a number one greater than the maximum
  possible (i.e. 2n or 256 for a byte)
• For example,

(123)10 (01111011)2 (-123)10 (10000101)2
(133)10 (256-123)10
12
Frequently Asked Question

• So how can you tell the difference between

(-123)10 (10000101)2 and (133)10
(10000101)2

• You cant unless you know whether youre using
  signed or unsigned arithmetic

13
Hexadecimal

• Base 16
• Sixteen digits, 0-9 and A-F (ten to fifteen)
• Columns represent (from right to left) units,
  16s, 256s, 4096s etc.

7B
7161 11160 123
14
Decimal to Hex Conversion
Converting (123)10 into hex
123 16 7 remainder 11 (or B) 7
16 0 remainder 7
Answer (123)10 (7B)16
15
Binary to Hex / Hex to Binary
Each group of four binary bits maps on to a
single hex digit.

• Even very long numbers can be converted easily,
  treating each hex digit independently.

16
Binary Arithmetic - Addition

• Binary long addition works just like decimal long
  addition.

1
0
0
1
1
1

0
0
1
1
1
0
0
Carried digits
1
Result

17
Full Adder

• Each column of the sum has three inputs
• Digits from the two numbers to add (A and B)
• Carry bit from previous column
• It also has two outputs
• Result bit
• Carry bit to next column
• These are the logical operations performed by a
  full adder circuit.

18
Parallel Adder

• To add two n-bit numbers together, n full-adders
  should be cascaded.
• Each full-adder represents a column in the long
  addition.

19
Summary

• In digital electronics, numbers are represented
  using base-2 (binary).
• Base-16 (hex) is often used by human programmers
  as binary to hex conversion is very easy.
• Binary numbers may be unsigned or signed (twos
  complement).
• Binary addition works in a similar way to decimal
  long addition.