Lecture No. 4
Number Systems
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Arithmetic Operations - Digital Logic Design - Lecture Slides, Slides of Digital Logic Design and Programming
Arithmetic operations, Floating point numbers, Hexadecimal Arithmetic, Octal Number System, Counting in Octal, Binary Octal Conversion, Octal Addition and Subtraction are main points of this lecture.
Typology: Slides
2011/2012
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Lecture No. 4
Number Systems
32-bit f.p. number (recap)
32-bit Floating point format
Sign bit 1
Exponent bits 8
Mantissa bits 23
Exponent represented as Biased 127
Arithmetic operations on
floating point numbers
Addition
Adding mantissas after adjusting exponents
Subtraction
Subtracting mantissas after adjusting exponents
Multiplication
Multiplying mantissas and adding exponents
Division
Dividing mantissas and subtracting exponents
64-bit f.p. number (recap)
64-bit Double-Precision floating Point
format
Sign bit 1
Exponent bits 11
Mantissa bits 52
Exponent represented as Biased 1023
Hexadecimal Numbers (recap)
H exadecimal Number System
Base 16 number system
0 to F
Used to represent large binary numbers
Counting in Hexadecimal
(recap)
Decimal Binary Hexadecimal Decimal Binary Hexadecimal
0 0000 0 8 1000 8
1 0001 1 9 1001 9
2 0010 2 10 1010 A
3 0011 3 11 1011 B
4 0100 4 12 1100 C
5 0101 5 13 1101 D
6 0110 6 14 1110 E
7 0111 7 15 1111 F
Hexadecimal-decimal
conversion (recap)
Hexadecimal to Decimal Conversion
Indirect Method
Hexadecimal →Binary → Decimal
Sum-of-Weights
Decimal-Hexadecimal
Conversion (recap)
Decimal to Hexadecimal Conversion
Indirect Method
Decimal →Binary → Hexadecimal
Repeated Division by 16
Octal Number System
Base 8
Representing Binary in compact form
Not commonly used in the presence of
Hexadecimal Number System
Counting in Octal
Octal digit represented by a 3-bit binary
Decimal 8 represented by 2-digit Octal
Counting in Octal
Decimal Octal Decimal Octal Decimal Octal
8 10 16 20 24 30
9 11 17 21 25 31
10 12 18 22 26 32
11 13 19 23 27 33
12 14 20 24 28 34
13 15 21 25 29 35
14 16 22 26 30 36
15 17 23 27 31 37
Binary-Octal Conversion
Binary to Octal Conversion
Octal to Binary Conversion
Decimal-Octal Conversion
Decimal to Octal Conversion
Indirect Method
Decimal →Binary → Octal
Repeated Division by 8
Octal Addition & Subtraction