Perform the following conversions : a. 101010 (base 2) to base 10 answer b. ca (base 16) to base 10 answer c. 10101011 (base 2) to base 16 answer d. 50 (base 10) to base 2 answer e. f8 (base 16) to base 2 answer

(1) 42 base 10

(2) 202 base 10

(3) AB base 16

(4)110010 base 2

(5) 11111000 base 2

Explanation:

(1)

Step 1: Write down the binary number:

101010

Step 2: Multiply each digit of the binary number by the corresponding power of two:

1x25 + 0x24 + 1x23 + 0x22 + 1x21 + 0x20

Step 3: Solve the powers:

1x32 + 0x16 + 1x8 + 0x4 + 1x2 + 0x1 = 32 + 0 + 8 + 0 + 2 + 0

Step 4: Add up the numbers written above:

32 + 0 + 8 + 0 + 2 + 0 = 42. This is the decimal equivalent of the binary number 101010.

(2)

Step 1: Write down the hexadecimal number:

(CA)16

Step 2: Show each digit place as an increasing power of 16:

Cx161 + Ax160

Step 3: Convert each hexadecimal digits values to decimal values then perform the math:

12x16 + 10x1 = (202)10

(3)

Step 1: Write down the binary number:

10101011

Step 2: Group all the digits in sets of four starting from the LSB (far right). Add zeros to the left of the last digit if there aren't enough digits to make a set of four:

1010 1011

Step 3: Use the table below to convert each set of three into an hexadecimal digit:

1010 = A, 1011 = B

So, AB is is the hexadecimal equivalent to the decimal number 10101011.

To convert from binary to hexadecimal use the following table:

Bin:00000001001000110100010101100111

Hexa:01234567

Bin:10001001101010111100110111101111

Hexa:89ABCDEF

(4)

Step 1: Divide (50)10 successively by 2 until the quotient is 0:

50/2 = 25, remainder is 0

25/2 = 12, remainder is 1

12/2 = 6, remainder is 0

6/2 = 3, remainder is 0

3/2 = 1, remainder is 1

1/2 = 0, remainder is 1

(5)

Step 1: Divide (50)10 successively by 2 until the quotient is 0:

50/2 = 25, remainder is 0

25/2 = 12, remainder is 1

12/2 = 6, remainder is 0

6/2 = 3, remainder is 0

3/2 = 1, remainder is 1

1/2 = 0, remainder is 1

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