Answer:
(1) 42 base 10
(2) 202 base 10
(3) AB base 16
(4)110010 base 2
(5) 11111000 base 2
Step-by-step 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: 0000 0001 0010 0011 0100 0101 0110 0111
Hexa: 0 1 2 3 4 5 6 7
Bin: 1000 1001 1010 1011 1100 1101 1110 1111
Hexa: 8 9 A B C D E F
(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