Fundamentals of Programming Lecture 2 Hamed Rasifard Outline - - PowerPoint PPT Presentation

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Mar 12, 2023 420 likes •564 views

Fundamentals of Programming Lecture 2 Hamed Rasifard Outline Numerical Systems Converting Numbers Summation and Subtraction of Binary Numbers Numerical Systems Binary (base 2) Octal (base 8) Decimal (Base 10)

SLIDE 1

Fundamentals of Programming

Lecture 2 Hamed Rasifard

SLIDE 2

Outline

Numerical Systems
Converting Numbers
Summation and Subtraction of Binary

Numbers

SLIDE 3

Numerical Systems

Binary (base 2)
Octal (base 8)
Decimal (Base 10)
Hexadecimal (Base 16)

SLIDE 4

Digits

Binary Octal Decimal Hexadecimal

1 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7 8 8 9 9 A B C D E F

SLIDE 5

Numbers & Notation

Numbers:

Binary: 101, 1100, 1001, 10011 Decimal: 101, 676, 245, 1470 Octal: 101, 345, 777 Hexadecimal:101, 234, 547E, A45CF

Notation

Mention base: (101)2, (101)10, (345)8

SLIDE 6

Positional Value

(747)10 = (7*100 + 4*10 + 7*1)10
(101)2 = (1*100 + 0*10 + 1*1)2
(457)8 = (4*100 + 5*10 + 7*1)8

SLIDE 7

Bits & Bytes

Memories consists of bits
Each bit could keep 0 or 1
Every 8 bits make a Byte

SLIDE 8

Converting Binary Numbers to Octal and Hexadecimal Numbers

Binary to Octal: Separate each 3 Bits

and rewrite their equivalents

(101011)2 (53)8

Binary to Hexadecimal: Separate each 4

Bits and rewrite their equivalents

(101011)2 (2B)16

SLIDE 9

Octal to Binary: write 3 binary digits for

every octal digits

(653)8 (110101011)2

Hexadecimal to Binary: write 4 binary

digits for every octal digits

(FAD5)16 (1111101011010101)2

Converting Octal and Hexadecimal Numbers to Binary Numbers

SLIDE 10

Express base positional values in

decimal

(1*100 + 0*10 + 1*1)2=(1*22 + 0*21 + 1*20)10 (1*100 + 0*10 + 1*1)8=(1*82 + 0*81 + 1*80)10 (1*100 + 0*10 + 1*1)16=(1*162 + 0*161 + 1*160)10

Converting Octal and Hexadecimal and Binary to Decimal

SLIDE 11

write the positional values of the

columns right to left

Find a column whose positional value

is greater than the decimal number

From the leftmost column to the right

divide number to positional values

Converting Decimal to Octal and Hexadecimal and Binary

SLIDE 12

Represent Negative Numbers in Computer Systems

Bit-Sign
One’s complement notation
Two’s complement notation

SLIDE 13

Summation and Subtraction in Computer Systems

Summation: Just ordinary add(consider
verflow)
Subtraction: Add first number to two’s