CSE 102 Introduction to Computer Engineering

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CSE 102Introduction to Computer Engineering

• Number System

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Number Systems

• Binary numbers (Base 2) 0,1
• Octal numbers (Base 8) 0,1,2,3,4,5,6,7
• Decimal numbers (Base 10) 0,1,2,3,4,5,6,7,8,9
• Hexadecimal numbers (Base 16) 0,1,2,3,4,5,6,7,8,
  9,A,B,C,D,E,F

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Decimal to Binary Conversion

• (102)10 (?)2
• (1100110)2

Divide by 2 Remainder
102 2
51 2 0
25 2 1
12 2 1
6 2 0
3 2 0
1 2 1
0 2 1
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Decimal to Binary Conversion

• (0.125)10 (?)2
• (0.001)2

Multiply by 2 Integer part
0.125 2
0.25 2 0
0.5 2 0
1.0 2 1
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Decimal to Binary Conversion
Multiply by 2 Integer part
0.4 2
0.8 2 0
1.6 2 1
1.2 2 1
0.4 2 0
0.8 2 0
1.6 2 1
1.2 2 1
0.4 2 0

• (0.4)10 (?)2
• (0.01100110)2
• (0.0110)2

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Binary to Octal and Hexadecimal Conversion

• Octal (1100110)2 (?)8
• (001100110)2 (146)8
• 1 4 6
• Hexadecimal (1100110)2 (?)16
• (01100110)2 (66)16
• 6 6

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Binary to Octal and Hexadecimal Conversion

• Octal (0.01100110)2 (?)8
• (0.011001100)2 (0.314)8
• 3 1 4
• Hexadecimal (0.01100110)2 (?)16
• (0.01100110)2 (66)16
• 6 6

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Representation of Integers

• Signed-magnitude representation
• 2s complement representation

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Signed-magnitude Representation
sign bit 0-positive 1-negative
integer

• Ex 10210
• - 10210

0 0 0 0 1 1 0 0 1 1 0
1 0 0 0 1 1 0 0 1 1 0
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2s complement Representation

• To find 1s complement of a binary number change
  1s to 0s and 0s to 1s
• To find 2s complement of a number add 1 to its
  1s complement
• Ex (102)10 (0001100110)2
• 1s complement 1110011001
• 2s complement 1110011010

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2s complement Representation

• Ex
• 10210
• -10210

0 0 0 1 1 0 0 1 1 0
1 1 1 0 0 1 1 0 1 0