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maks197457 [2]
2 years ago
7

Question No. 5:

Computers and Technology
1 answer:
Mkey [24]2 years ago
8 0

Answer:

The answers are:

a) (1001111)_2 = (79 )_{10}\\b) (11000001)_2 = (C1 )_{16}\\c) (E16)_{16} = ( 3606)_{10}\\d) (56)_{10} = (38 )_{16}\\e) (63)_{10}= (111111 )_2

Explanation:

<u>a. (1001111) 2 = ( ) 10</u>

In order to convert a base 2 number to base 10 number system the place values are used.

the procedure is as follows:

(1001111)_2\\=(1*2^6)+(0*2^5)+(0*2^4)+(1*2^3)+(1*2^2)+(1*2^1)+(1*2^0)\\=(1*64)+(0*32)+(0*16)+(1*8)+(1*4)+(1*2)+(1*1)\\=64+0+0+8+4+2+1\\=79

<u>b) (11000001) 2 = ( ) 16</u>

In order to convert a base 2 number into base 16, group of 4-bits are made starting from right to left

The groups from the given number are:

1100 0001

Then the groups are changed in to decimal/hexa

So,

(1100)_2 = (1*2^3)+(1*2^2)+(0*2^1)+(0*2^0)\\=(1*8)+(1*4)+(0*2)+(0*1)\\=8+4+0+0=12=C\\\\0001=1

Writing in the same order in which groups were:

(C1)_{16}

<u>c) (E16) 16 = ( ) 10</u>

(E16)_{16}\\=(E*16^2)+(1*16^1)+(6*16^0)\\=(E*256)+(1*16)+(6*1)\\=3584+16+6\\=3606

<u>d) (56) 10 = ( ) 16</u>

Dividing by 16 and noting remainders

16        56

           3 - 8

So,

The number in base 16 is 38

<u>e) (63) 10 = ( ) 2</u>

Dividing by 2

2         63

2         31 - 1

2         15 - 1

2          7 -  1

2          3 -  1

            1 - 1

So the  number after converting in base 2 is:

111111

Hence,

The answers are:

a) (1001111)_2 = (79 )_{10}\\b) (11000001)_2 = (C1 )_{16}\\c) (E16)_{16} = ( 3606)_{10}\\d) (56)_{10} = (38 )_{16}\\e) (63)_{10}= (111111 )_2

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