Introduction to Computing: A Foundation for Embedded Systems Design, Lecture notes of Embedded Systems

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Embedded Systems Design

1

Topic

Introduction to Computing

2

COMPUTING 4

• (^) Gates
• (^) Decision Making Operators
• (^) Number Representation
• (^) Adder/Subtractor
• (^) Memorizing Elements
• (^) Towards a Processor
• (^) Inside the CPU

Outline

COMPUTING 5

Gates

Logic Gates

COMPUTING 7

• (^) Gates
• (^) Decision Making Operators
• (^) Number Representation
• (^) Adder/Subtractor
• (^) Memorizing Elements
• (^) Towards a Processor
• (^) Inside the CPU

Outline

COMPUTING 8

s 1 s0 y 0 0 a 0 1 b 1 0 c 1 1 d

Multiplexer

Decision/Selection Operators

Decision Making Operators

COMPUTING 10

• (^) Gates
• (^) Decision Making Operators
• (^) Number Representation
• (^) Adder/Subtractor
• (^) Memorizing Elements
• (^) Towards a Processor
• (^) Inside the CPU

Outline

COMPUTING 11

Number Representation

Unsigned Number Representation

 General Rule for Unsigned Representation of a system having x as

base (where x is 2 in binary system, 8 in octal system 10 in decimal

system and 16 in hexadecimal system)

 In x-base system total x characters to represent a number e.g in Binary

(base 2) 0 and 1 to represent a number , in octal 0 to 7, in decimal 0-

and 0-9, A-F in hexadecimal system.

x

n-

……x

3

x

2

x

1

x

0

Integer

. x

x

x

x

x

……. x

-m

. Fractional

COMPUTING 13

Number Representation

Unsigned Number Representation Range of Unsigned number = 2 no. of bits

• 1 e.g. if no. of bits are 3 then range is = 2 3
• 1 = 7 22 21 20 Decimal Number 0 0 0 0 0 0 1 1 0 1 0 2 0 1 1 3 1 0 0 4 1 0 1 5 1 1 0 6 1 1 1 7

What to do with Singed number which can be positive or negative

COMPUTING 14

Number Representation

Signed Number Representation Signed Magnitude Representation S 21 20 Decimal Number 0 0 0 + 0 0 1 + 0 1 0 + 0 1 1 + 1 0 0 - 1 0 1 - 1 1 0 - 1 1 1 - Decimal Number 0 0 0 + 0 0 1 + 0 1 0 + 0 1 1 + 1 0 0 - 1 0 1 - 1 1 0 - 1 1 1 - 1’s Compliment Representation

COMPUTING 16

• (^) Gates
• (^) Decision Making Operators
• (^) Number Representation
• (^) Adder/Subtractor
• (^) Memorizing Elements
• (^) Towards a Processor
• (^) Inside the CPU

Outline

COMPUTING 17

Arithmetic Operators

1- Bit Binary Half Adder

A B S C 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 1 S C Half Adder

S

C

A

B

Note: Operand of One Bits Total Sum of two bits i.e 1 bit sum and 1 bit carry

Adder/Subtractor

COMPUTING 19

Adder/Subtractor

Subtractor:

To get C = A-B we can do C= A + (-B)

How –B can be achieved

• (^) Take 1’s Complement of ‘B’ by inverting each bit
• (^) Add 1 to 1’s complement of ‘B’

Can we modify adder circuit to behave as combined adder/subtractor.???

Yes why not …

Arithmetic Operators

COMPUTING 20

Arithmetic Operators

Adder/Subtractor

Combined Adder/Subtractor:

1. When addition we need Cin = 0 and B is transferred as it is to FA.

2. When subtraction is required we put Cin = 1 and it do two things:

1. Inverts each bit of B as b xor 1 = b’

2. Add one to result as Cin = 1

3. Hence S = A + (B’ + 1) = A + (- B)

And this is what we need to perform 2’s complement of B