Answer:
The answer is A4B₁₆ = 2635₁₀ = 101001001011₂
Explanation:
To convert from hexadecimal base system to binary base system, first you can do an intermediate conversion from hexadecimal to decimal using this formula:
where position of the x₁ is the rightmost digit of the number and the equivalents hexadecimal numbers to decimal:
- A = 10.
- B = 11.
- C = 12.
- D = 13.
- E = 14.
- F = 15.
A4B₁₆ = A*16²+4*16¹+B*16⁰ = 2560 + 64 + 11 = 2635₁₀
Now, you have the number transformed from hexadecimal to decimal. To convert the decimal number 2635 to binary: Divide the number repeatedly by 2, keeping track of each remainder, until we get a quotient that is equal to 0:
2635 ÷ 2 = 1317 + 1;
1317 ÷ 2 = 658 + 1;
658 ÷ 2 = 329 + 0;
329 ÷ 2 = 164 + 1;
164 ÷ 2 = 82 + 0;
82 ÷ 2 = 41 + 0;
41 ÷ 2 = 20 + 1;
20 ÷ 2 = 10 + 0;
10 ÷ 2 = 5 + 0;
5 ÷ 2 = 2 + 1;
2 ÷ 2 = 1 + 0;
1 ÷ 2 = 0 + 1;
Now, construct the integer part base 2 representation, by taking the remainders starting from the bottom of the list:
2635₁₀ = 101001001011₂
