CS101 Introduction to Computing
Lecture 8
Binary Numbers & Logic Operations
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Binary Numbers and Logic Operations - Introduction to Computing - Lecture Slides, Slides of Introduction to Computing
Binary Numbers, Logic Operations, Decimal to binary conversions, Fundamental operations, Understand the NOT, AND, OR and XOR, popular number systems, Boolean Logic Operations and some other terms as well as topics are also part of this lecture.
Typology: Slides
2011/2012
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CS101 Introduction to Computing
Lecture 8
Binary Numbers & Logic Operations
The focus of the last lecture was on the microprocessor
- During that lecture we learnt about the function of the central component of a computer, the microprocessor
- And its various sub-systems
- Bus interface unit
- Data & instruction cache memory
- Instruction decoder
- ALU
- Floating-point unit
- Control unit
BINARY
(BASE 2)
numbers
DECIMAL
(BASE 10)
numbers
Binary (base 2) number system consists of just two
Other popular number systems
- Octal
- base = 8
- 8 symbols (0,1,2,3,4,5,6,7)
- Hexadecimal
- base = 16
- 16 symbols (0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F)
Decimal (base 10) numbers are expressed in the positional notation
4202 = 2x10^0 + 0x10^1 + 2x10^2 + 4x10^3
1’s multiplier
1
Decimal (base 10) numbers are expressed in the positional notation
4202 = 2x10^0 + 0x10^1 + 2x10^2 + 4x10^3
10’s multiplier
10
Decimal (base 10) numbers are expressed in the positional notation
4202 = 2x10^0 + 0x10^1 + 2x10^2 + 4x10^3
1000’s multiplier
1000
Binary (base 2) numbers are also expressed in the positional notation
10011 = 1x2^0 + 1x2^1 + 0x2^2 + 0x2^3 + 1x2^4
The right-most is the least significant digit
The left-most is the most significant digit
Binary (base 2) numbers are also expressed in the positional notation
10011 = 1x2^0 + 1x2^1 + 0x2^2 + 0x2^3 + 1x2^4
2’s multiplier
2
Binary (base 2) numbers are also expressed in the positional notation
10011 = 1x2^0 + 1x2^1 + 0x2^2 + 0x2^3 + 1x2^4
4’s multiplier
4
Binary (base 2) numbers are also expressed in the positional notation
10011 = 1x2^0 + 1x2^1 + 0x2^2 + 0x2^3 + 1x2^4
16’s multiplier
16
Counting in Decimal
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
20 21 22 23 24 25 26 27 28 29
30 31 32 33 34 35 36 . . .
0 1 10 11 100 101 110 111 1000 1001
1010 1011 1100 1101 1110 1111 10000 10001 10010 10011
10100 10101 10110 10111 11000 11001 11010 11011 11100 11101
11110 11111 100000 100001 100010 100011 100100 . . .