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Compute the decimal representation for each of the following numbers.

a. (1100110)2
b. (346)7
c. (1024)8
d. (3B2)16
e. (AF72)16
f. (120121)3
g. (A22)11

User JaKXz
by
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1 Answer

1 vote

Answer:


(1100110)_2= 102_{10


(346)_7= 181_{10


(1024)_8 = 532_{10


(3B2)_(16) = 946_{10


(AF72)_(16)= 44914_{10


(120121)_3= 421_{10


(A22)_(11) = 1234_(10)

Step-by-step explanation:

Required

Convert to decimal

To do this we get the position of individual digits (starting from the rightmost digit).

Then each digit is multiplied by the base raise to power its position.

Lastly, we sum the results of the products.

Following the above steps, we have:


a.\ (1100110)_2


= 1 * 2^6 + 1 * 2^5 + 0 * 2^4 + 0 * 2^3 + 1 * 2^2 + 1 * 2^1 + 0 * 2^0


= 1 * 64 + 1 * 32 + 0 * 16 + 0 * 8 + 1 * 4 + 1 * 2 + 0 * 1


= 64 + 32 + 0 + 0 + 4 + 2 + 0


= 102

Hence:


(1100110)_2= 102_{10


b.\ (346)_7


= 3 * 7^2 + 4*7^1 + 6 * 7^0


= 3 * 49 + 4*7 + 6 * 1


= 147 + 28 + 6


= 181

Hence:


(346)_7= 181_{10


c.\ (1024)_8


= 1 * 8^3 + 0 * 8^2 + 2 * 8^1 + 4 * 8^0


= 1 * 512+ 0 * 64 + 2 * 8 + 4 * 1


= 512+ 0 + 16 + 4


= 532

Hence:


(1024)_8 = 532_{10


d.\ (3B2)_{16


= 3 * 16^2 + B * 16^1 + 2 * 16^0


= 3 * 256 + B * 16 + 2 * 1

B represents 11, so we have:


= 3 * 256 + 11 * 16 + 2 * 1


= 768 + 176 + 2


= 946

Hence:


(3B2)_(16) = 946_{10


e.\ (AF72)_{16


= A * 16^3 + F * 16^2 + 7 * 16^1 + 2 * 16^0


= A * 4096 + F * 256 + 7 * 16 + 2 * 1

A represents 10 and F, 15; So, we have:


= 10 * 4096 + 15 * 256 + 7 * 16 + 2 * 1


= 40960 + 3840 + 112 + 2


= 44914

Hence:


(AF72)_(16)= 44914_{10


f.\ (120121)_3


= 1 * 3^5 + 2*3^4 + 0*3^3 + 1*3^2 + 2*3^1 + 1*3^0


= 1 * 243 + 2*81 + 0*27 + 1*9 + 2*3 + 1*1


= 243 + 162 + 0 + 9 + 6 + 1


= 421

Hence:


(120121)_3= 421_{10


g.\ (A22)_{11


= A * 11^2 + 2 * 11^1 + 2 * 11^0


= A * 121 + 2 * 11 + 2 * 1

A represents 10, so we have:


= 10 * 121 + 2 * 11 + 2 * 1


= 1210 + 22+ 2


= 1234

Hence:


(A22)_(11) = 1234_(10)

User Neo
by
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