# CSE 241 Lecture Notes - Lecture 2: Number One Crossbar Switching System, Decimal Mark

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CSE 241

Recitation 2

Example: Converting Arbitrary Bases to Decimal

1.3a (4310)5 -> (?)10

4 x 53 + 3 x 52 + 1 x 51 + 0 x 50

500 + 75 + 5 + 0 = (580)10

(435)6 -> (?)10

4 x 62 + 3 x 61 + 5 x 60

144 + 18 + 5 = (167)10

Example: Determine the base of the numbers such that an equation is true.

(24)b + (17)b = (40)b

(2xb + 4x1) + (1xb + 7x1) = (4xb + 0x1)

2b + 4 + b + 7 = 4b

3b + 11 = 4b

11 = b

Check (convert back to decimal and make sure that it still makes sense):

(22+4) + (11+7) = (44)

26 + 18 = 44

44 = 44

x2 ā (b + 1)x + (2b + 2) = 0

x = (3)b x = (6)b

In base b: 6 + 3 = 11, 6 x 3 = 22

6 + 3 = 1b + 1 6 x 3 = 2b + 2

8 = b 16 = 2b

8 = b

Example: Converting Decimal Numbers to Binary

(1.125)10 Deal with this in two segments on either side of the decimal point.

(1)10 = (1)2

2 x 0.125

2 x 0.250 0

2 x 0.500 0

2 x 0.000 1 (0.125)10 = (0.001)2

(1.001)2

(123)10

2 | 123

2 | 61 1

2 | 30 1

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