Question

Express the following binary numbers in hexadecimal. (a) %100011100101 (b) %1011001111 (show work)

Answer 1

Answer:

$(100011100101)_{2} = (8E5)_{16} = %8E5$

$(1011001111) = (2CF)_{16} = %2CF$

Explanation:

Binary and hexadecimal values have the following pair equivalences.

$(0000)_{2} = (0)_{16}$

$(0001)_{2} = (1)_{16}$

$(0010)_{2} = (2)_{16}$

$(0011)_{2} = (3)_{16}$

$(0100)_{2} = (4)_{16}$

$(0101)_{2} = (5)_{16}$

$(0110)_{2} = (6)_{16}$

$(0111)_{2} = (7)_{16}$

$(1000)_{2} = (8)_{16}$

$(1001)_{2} = (9)_{16}$

$(1010)_{2} = (A)_{16}$

$(1011)_{2} = (B)_{16}$

$(1100)_{2} = (C)_{16}$

$(1101)_{2} = (D)_{16}$

$(1110)_{2} = (E)_{16}$

$(1111)_{2} = (F)_{16}$

We convert from binary to hexadecimal selecting groups of 4 binary from the binary code, from the least significant bits(at the right) to the most significant bits(at the left). The conversion is an hexadecimal "string" from the last group you converted to the first. So:

(a) %100011100101

$(0101)_{2} = (5)_{16}$

$(1110)_{2} = (E)_{16}$

$(1000)_{2} = (8)_{16}$

So

$(100011100101)_{2} = (8E5)_{16}$

(b) %1011001111

$(1111)_{2} = F_{16}$

$(1100)_{2} = C_{16}$

$(10)_{2} = (0010)_{2} = 2_{16}$

$(1011001111) = (2CF)_{16}$