Question

1) 55(10)=x(2) 2) 14(10)=x(8) 2) 127(8)=x(10) 3) 1E(16)=x(10) 4) 100110(2)=x(10) 5) 101,1(2)=x(10)

Answer 1

Ответ:

1. 550=2x

x=275

2. 140=8x

x=17.5

Answer 2

To convert numbers from one base to another, you can use the following methods:

1. From base 10 to another base: To convert a number from base 10 (decimal) to another base, you can use repeated division by the target base. Here are the conversions for your given examples:

   1. 55(10) = x(2) (Convert to binary): 55 / 2 = 27 remainder 1 27 / 2 = 13 remainder 1 13 / 2 = 6 remainder 1 6 / 2 = 3 remainder 0 3 / 2 = 1 remainder 1 1 / 2 = 0 remainder 1

      Read the remainders in reverse order to get the binary representation: 55(10) = 110111(2).

   2. 14(10) = x(8) (Convert to octal): 14 / 8 = 1 remainder 6

      The octal representation is simply the remainders in reverse order: 14(10) = 16(8).

   3. 127(8) = x(10) (Convert to decimal): 78^0 + 28^1 + 1*8^2 = 7 + 16 + 64 = 87(10).

   4. 1E(16) = x(10) (Convert to decimal): E in hexadecimal represents 14 in decimal. So, 1E(16) = 116^1 + 1416^0 = 16 + 14 = 30(10).

   5. 100110(2) = x(10) (Convert to decimal): 12^5 + 02^4 + 02^3 + 12^2 + 12^1 + 02^0 = 32 + 0 + 0 + 4 + 2 + 0 = 38(10).

2. From another base to base 10: To convert a number from another base to base 10, you can use the weighted sum method, where each digit is multiplied by the base raised to the power of its position (from right to left) and then summed up.

   5. 101.1(2) = x(10) (Convert binary to decimal): 12^2 + 02^1 + 12^0 + 12^-1 = 4 + 0 + 1 + 0.5 = 5.5(10).

So, the conversions are:

1. 55(10) = 110111(2)
2. 14(10) = 16(8)
3. 127(8) = 87(10)
4. 1E(16) = 30(10)
5. 101.1(2) = 5.5(10)