Question

convert the following binary number (base 2) to hexadecimal (base 16).
10000100₂=
(base 16)
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question 9
add the following using binary addition:
10011(2)+111(2)=
(2)
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question 10
add the following using binary addition:
110(2)+10(2)=
(2)
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question 11

Explanation:

Question 8: Convert binary to hexadecimal

Step1: Group binary digits

Group the binary number \(10000100_2\) into groups of 4 from the right: \(1000\) \(0100\).

Step2: Convert each group to hexadecimal

• For \(1000_2\): \(1\times2^3+0\times2^2 + 0\times2^1+0\times2^0=8\)
• For \(0100_2\): \(0\times2^3+1\times2^2 + 0\times2^1+0\times2^0 = 4\)

Question 9: Binary addition \(10011_2+111_2\)

Step1: Align the numbers

  10011
+   111

Step2: Add bit - by - bit

Starting from the rightmost bit:

• \(1 + 1=10\) (write \(0\), carry \(1\))
• \(1+1 + 1=11\) (write \(1\), carry \(1\))
• \(0+1+1 = 10\) (write \(0\), carry \(1\))
• \(0 + 0+1=1\)
• \(1+0 = 1\)

Question 10: Binary addition \(110_2+10_2\)

Step1: Align the numbers

  110
+  10

Step2: Add bit - by - bit

Starting from the rightmost bit:

• \(0+0 = 0\)
• \(1+1=10\) (write \(0\), carry \(1\))
• \(1+0 + 1=10\)

Answer:

• Question 8: \(84_{16}\)
• Question 9: \(11010_2\)
• Question 10: \(1000_2\)