Question

Convert A4B from hexadecimal to binary. Show your work.

Answer 1

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