Answer:
a.
101010 base 2 = 42 base 10
101010 in base 2 = 2A in base 16.
b.
101010 in base 10 = 11000101010010010 base 2
101010 in base 10 = 18A92
c.
101010 base 16 = 1,052,688 base 10
101010 base 16 = 100000001000000010000 base 2
Explanation:
Conversion to Base 10
The general steps for converting a base 10 or "normal" number into another base are: First, divide the number by the base to get the remainder. This remainder is the first, ie least significant, digit of the new number in the other base. Then repeat the process by dividing
Conversion from Base 10 to any base
The general steps for converting a base 10 or "normal" number into another base are:
First, divide the number by the base to get the remainder. This remainder is the first, ie least significant, digit of the new number in the other base
Then repeat the process by dividing the quotient of step 1, by the new base. This time, the remainder is the second digit, ie the second least significant.
Repeat this process until your quotient becomes less than the base. This quotient is the last digit, ie the most significant digit.
Conversion between bases other than base 10
First, we convert to base 10 then we convert from base 10 to the base we intend to convert to
Now, we proceed to questions
a. 101010 in base 2.
Conversion to base 10
101010 = 1 * 2^5 + 0 * 2⁴ + 1 *2³ + 0 * 2² + 1 * 2¹ + 0 * 2°
101010 = 1 * 32 + 0 + 1 *8 + 0 + 1 * 2 + 0
101010 = 32 + 8 + 2
101010 base 2 = 42 base 10
Conversion to base 16
First, we convert to base 10 ---- 42 (Calculated)
Then we convert to base 16
42/16 = 2 Remainder 10
2/16 = 0 Remainder 2
We start writing the number from bottom
2(10) .
10 in hexadecimal is represented by letter A
So, we have 2A
101010 in base 2 = 2A in base 16.
b. 101010 in base 10
Conversion to base 2
101010/2 = 50505 Remainder 0
50505/2 = 25252 Remainder 1
25252/2 = 12626 Remainder 0
12626/2 = 6313 Remainder 0
6313/2 = 3156 Remainder 1
3156/2 = 1578 Remainder 0
1578/2 = 789 Remainder 0
789/2 = 394 Remainder 1
394/2 = 197 Remainder 0
197/2 = 98 Remainder 1
98/2 = 49 Remainder 0
49/2 = 24 Remainder 1
24/2 = 12 Remainder 0
12/2 = 6 Remainder 0
6/3 = 3 Remainder 0
3/2 = 1 Remainder 1
1/2 = 0 Remainder 1
We start counting from the bottom
11000101010010010 base 2
Conversion to Base 16
101010/16 = 6313 Remainder 2
6313/16 = 394 Remainder 9
394/16 = 24 Remainder 10
24/16 = 1 Remainder 8
1/16 = 0 Remainder 1
We start counting from the bottom
18(10)92
10 is represented with A
18A92
c. 101010 in base 16
Conversion to Base 10
101010 = 1 * 16^5 + 0 * 16⁴ + 1 * 16³ + 0 * 16² + 1 * 16¹ + 0 * 16°
101010 = 1,048,576 + 0 + 4,096 + 0 + 16 + 0
101010 = 1,052,688 base 10
Conversion to base 2
1,052,688/2 = 526344 Remainder 0
526344/2 = 263172 Remainder 0
263172/2 = 131586 Remainder 0
131586/2 = 65793 Remainder 0
65793/2 = 32896 Remainder 1
32896/2 = 16448 Remainder 0
16448/2 = 8224 Remainder 0
8224/2 = 4112 Remainder 0
4112/2 = 2056 Remainder 0
2056/2 = 1028 Remainder 0
1028/2 = 514 Remainder 0
514/2 = 257 Remainder 0
257/2 = 128 Remainder 1
128/2 = 64 Remainder 0
64/2 = 32 Remainder 0
32/2 = 16 Remainder 0
16/2 = 8 Remainder 0
8/2 = 4 Remainder 0
4/2 = 2 Remainder 0
2/2 = 1 Remainder 0
1/2 = 0 Remainder 1
We start from the bottom
= 100000001000000010000 base 2
