Question

By substituting the value of x in the following, first compute y and then represent y in Radix and Diminished-Radix complement formats (for respective Radix),

iii (x)10 + (1011)2 = ( y )8

iv (x)10 × (15)8 = ( y )2 

value of x is 49

Answer 1

Part iii

(1011)₂ = 11₁₀

$\underline{\begin{array}{cc} \space \space \space \space 490_{10} \\ + 011_{10} \end{array}}$ $\underline{\begin{array}{cc} X \\ + Y \end{array}}$

Z

$\underline{\begin{array}{cc} \space \space \space \space 490_{10} \\ + 011_{10} \end{array}}$

501₁₀

Hence discarding the leading 1 the result is 501.

Part iv

$\underline{\begin{array}{cc} \space \space \space \space 490_{10} \\ + 120_{10} \end{array}}$ $\underline{\begin{array}{cc} X \\ + Y \end{array}}$

Z

$\underline{\begin{array}{cc} \space \space \space \space 490_{10} \\ + 120_{10} \end{array}}$

610₁₀

Hence the result is 610