Convert the decimal number [latex] (2655)_{10} [/latex] into hexadecimal number.

[latex] \begin{aligned} (2655)_{16} &=2 \times 10^3+6 \times 10^2+5 \times 10^1+5 \times 10^0 \\ &=(2)_{16} \times(A)_{16}^3+(6)_{16} \times(A)_{16}^2+(5)_{16} \times(A)_{16}+(5) \end{aligned} [/latex] [latex] \begin{aligned} &b_3=a_3=(2)_{16} \\ &b_2=a_2+b_3 \beta=(6)_{16}+(2)_{16} \times(A)_{16}=(6)_{16}+(14)_{16}=(1 A)_{16} \\ &b_1=a_1+b_2 \beta=(5)_{16}+(1 A)_{16} \times(A)_{16}=(5)_{16}+(104)_{16}=(109)_{16} \\ &b_0=a_0+b_1 \beta=(5)_{16}+(109)_{16} \times(A)_{16}=(5)_{16}+(A 5 A)_{16}=(A 5 F)_{16} \end{aligned} [/latex]

Question 1.9: Convert the decimal number (2655)10 into hexadecimal number.

Numerical Methods: Fundamentals and Applications

Convert the decimal number $(2655)_{10}$ into hexadecimal number.

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\begin{aligned} (2655)_{16} &=2 \times 10^3+6 \times 10^2+5 \times 10^1+5 \times 10^0 \\ &=(2)_{16} \times(A)_{16}^3+(6)_{16} \times(A)_{16}^2+(5)_{16} \times(A)_{16}+(5) \end{aligned}

$\begin{aligned} &b_3=a_3=(2)_{16} \\ &b_2=a_2+b_3 \beta=(6)_{16}+(2)_{16} \times(A)_{16}=(6)_{16}+(14)_{16}=(1 A)_{16} \\ &b_1=a_1+b_2 \beta=(5)_{16}+(1 A)_{16} \times(A)_{16}=(5)_{16}+(104)_{16}=(109)_{16} \\ &b_0=a_0+b_1 \beta=(5)_{16}+(109)_{16} \times(A)_{16}=(5)_{16}+(A 5 A)_{16}=(A 5 F)_{16} \end{aligned}$