Date: Fri, 7 May 1999 15:05:36 -0600 (CST)
Sender: Larry
Subject: Base ten

Who is asking: Teacher
Level: All

Question:
101000112 is the same as what number in Base ten?

a. 83
b. 128
c. 93
d. 326
e. 163

How do you solve this type of problem?

Hi Larry

For the number 5036 in base 10 notation the digit 6 is in the units position, 3 is in the 10's position, 0 is in the 100's position and 5 is in the 1000's position. Thus, using the convention that 100 = 1,

5036 = 5x103 + 0x102 + 3x101 + 6x100

In base 2 notation we use powers of 2 rather than powers of 10, so for your problem 101000112,

power of the base 27262524 23222120
ceofficient 1010 0011

Thus

101000112 =1x27 + 0x26 + 1x25 + 0x24 + 0x23 + 0x22 + 1x21 + 1x20
 =1x128 + 0x64 + 1x32 + 0x16 + 0x8 + 0x4 + 1x2 + 1x1
 =163

The pattern is the same in any base, so for example

21035 =2x53 + 1x52 + 0x51 + 3x50
 =2x125 + 1x25 + 0x5 + 3x1
 =278
Cheers
Penny 		 

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