This document discusses number systems and binary arithmetic. It begins by explaining decimal and binary number representation, including place value and how to derive numbers in different bases. It then covers counting in binary, octal, and base-22 systems. Next, it discusses representing negative numbers using sign-magnitude, one's complement, and two's complement methods. Finally, it demonstrates binary addition and computation for both unsigned and signed numbers using two's complement.
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THIS PPT IS PRESENTED TO PROF. RAVITESH MISHRA FROM EC FINAL YEAR STUDENTS MADE FROM RAZAVI,DESIGN OF ANALOG CMOS INTEGRATED CIRCUITS ON DATAPATH SUBSYSTEM-MULTIPLICATION
FYBSC IT Digital Electronics Unit I Chapter I Number System and Binary Arithm...Arti Parab Academics
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FYBSC IT Digital Electronics Unit I Chapter I Number System and Binary Arithm...Arti Parab Academics
Number System:
Analog System, digital system, numbering system, binary number
system, octal number system, hexadecimal number system, conversion
from one number system to another, floating point numbers, weighted
codes binary coded decimal, non-weighted codes Excess – 3 code, Gray
code, Alphanumeric codes – ASCII Code, EBCDIC, ISCII Code,
Hollerith Code, Morse Code, Teletypewriter (TTY), Error detection
and correction, Universal Product Code, Code conversion.
Presentation for UG REsearch on Security.
Presented to Faculty in Charge of Siddaganga Institute of Technology, Tumkur, Karnataka, India
This is the first Presentation
1. NUMBER SYSTEM.pptx Computer Applications in PharmacyVedika Narvekar
B.Pharm SEM 2 Binary number system, Decimal number system, Octal
number system, Hexadecimal number systems, conversion decimal to
binary, binary to decimal, octal to binary etc, binary addition, binary
subtraction – One’s complement ,Two’s complement method, binary
multiplication, binary division
This contains detailed explanation of conversion of binary to decimal and decimal to binary. It also contains features of octal and hexadecimal number systems. An interactive slideshow. Full with animations and transitions... :) :)
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Lec2 Intro to Computer Engineering by Hsien-Hsin Sean Lee Georgia Tech -- Number system
1. ECE2030
Introduction to Computer Engineering
Lecture 2: Number System
Prof. Hsien-Hsin Sean LeeProf. Hsien-Hsin Sean Lee
School of Electrical and Computer EngineeringSchool of Electrical and Computer Engineering
Georgia TechGeorgia Tech
2. Decimal Number Representation
• Example: 90134 (base-10, used by Homo Sapien)
= 90000 + 0 + 100 + 30 + 4
= 9*104
+ 0*103
+ 1*102
+ 3*101
+ 4*100
• How did we get it?
901349013410
9013901310 44
90190110 33
909010 11
99 00
3. Generic Number Representation
• 90134
= 9*104
+ 0*103
+ 1*102
+ 3*101
+ 4*100
• A4A3A2A1A0 for base-10 (or radix-10)
= A4*104
+ A3*103
+A2*102
+A1*101
+A0*100
(A is coefficient; b is base)
• Generalize for a given number NN w/ base-bb
NN = An-1An-2 …A1A0
NN = An-1*bn-1
+ An-2*bn-2
+ … +A2*b2
+A0*b0
**Note that A < b**Note that A < b
11. 1
Base 16
• Decimal (base-10)
– (982)10
• Hexadecimal (base-16)
• Hey, what do we do when we
count to 10??
• 0
• 1
• 2
• 3
• 4
• 5
• 6
• 7
• 8
• 9
• 10
• 11
• 12
• 13
• 14
• 15
00
11
22
33
44
55
66
77
88
99
aa
bb
cc
dd
ee
ff
12. 2
Base 16
• (982)10= (3d6)16
• (3d6)16 can be written as (0011 1101 0110)2
• We use Base-16 (or Hex) a lot in computer
world
– Ex: A 32-bit address can be written as
0xfe8a7d200xfe8a7d20 ((0x0x is an abbreviation of Hex))
– Or in binary formOr in binary form
1111_1110_1000_1010_0111_1101_0010_00001111_1110_1000_1010_0111_1101_0010_0000
14. 4
Convert between different bases
• Convert a number base-x to base-y, e.g. (0100111)2 to (?)6
– First, convert from base-x to base-10 if x ≠ 10
– Then convert from base-10 to base-y
0100111 = 0∗26 + 1∗25 + 0∗24
+ 0∗23
+ 1∗22
+ 1∗21
+ 1∗20
= 39
39396
666 33
11 00
∴ (0100111)2 = (103)6
17. 7
Sign-magnitude
• Use the most significant bit (MSB)
to indicate the sign
– 00: positive, 11: negative
• Problem
– Representing zeros?
– Do not work in computation
• We will NOT use it in this course !
+0 000
+1 001
+2 010
+3 011
-3 111
-2 110
-1 101
0 100
18. 8
One’s Complement
• Complement (flip) each bit in a
binary number
• Problem
– Representing zeros?
– Do not always work in computation
• Ex: 111 + 001 = 000 → Incorrect !
• We will NOT use it in this course !
+0 000
+1 001
+2 010
+3 011
-3 100
-2 101
-1 110
0 111
19. 9
Two’s Complement
• ComplementComplement (flip) each bit in a
binary number and adding 1adding 1, with
overflow ignored
• Work in computation perfectly
• We will use it in this course !
011
100
One’s complement
3
101
Add 1
-3
010
One’s complement
101-3
011
Add 1
3
20. 0
Two’s Complement
• ComplementComplement (flip) each bit in a
binary number and adding 1adding 1, with
overflow ignored
• Work in computation perfectly
• We will use it in this course !
0 000
+1 001
-1 111
+2 010
-2 110
+3 011
-3 101
?? 100
100
011
One’s complement
100
Add 1
The same 100 represents
both 4 and -4
which is no good
21. 1
Two’s Complement
• ComplementComplement (flip) each bit in a
binary number and adding 1adding 1, with
overflow ignored
• Work in computation perfectly
• We will use it in this course !
0 000
+1 001
-1 1111
+2 010
-2 1110
+3 011
-3 1101
--4 1100
100
011
One’s complement
100
Add 1
MSB = 1 for negative
Number, thus 100
represents -4
22. 2
Range of Numbers
• An N-bit number
– Unsigned: 0 .. (2
N
-1)
– Signed: -2
N-1
.. (2
N-1
-1)
• Example: 4-bit
1110 (-8) 0111 (7)
Signed numbers
0000 (0) 1111 (15)Unsigned numbers
24. 4
Binary Computation
Unsigned arithmetic
101111 (47)
011111 (31)
---------------
001110 (78?? Due to overflow, note that
62 cannot be represented
by a 6-bit unsigned number)
The carry is
discarded
Signed arithmetic (w/ 2’s complement)
101111 (-17 since 2’s complement=010001)
011111 (31)
---------------
001110 (14)
The carry is
discarded
26. 6
Application of Two’s Complement
• The first Pocket CalculatorPocket Calculator “Curta”
used Two’s complement method for
subtractionsubtraction
• First complement the subtrahend
– Fill the left digits to be the same length
of the minuend
– Complemented number = (9 – digit)
• 4’s complement = 5
• 7’s complement = 2
• 0’s complement = 9
• Add 1 to the complemented number
• Perform an addition with the
minuend