Question

By substituting the value of x in the following, compute y and z  

(x)10 + (35) 8 = ( y ) 2 = ( z ) 16

ii (x)10 × (1010110) 2 = ( y ) 4 = ( z ) 10  

value of x is 29

Answer 1

Part i

$\underline{\begin{array}{cc} \space \space \space \space 290_{10} \\ + 280_{10} \end{array}}$ $\underline{\begin{array}{cc} X \\ + Y \end{array}}$

Z

$\underline{\begin{array}{cc} \space \space \space \space 290_{10} \\ + 720_{10} \end{array}}$

1010₁₀

Hence discarding the leading 1 the result is 10.

Part ii

(x)10 × (1010110) 2 = ( y ) 4 = ( z ) 10  

(1010110)₂=86₁₀

$\underline{\begin{array}{cc} \space \space \space \space 10_{10} \\ + 86_{10} \end{array}}$ $\underline{\begin{array}{cc} X \\ + Y \end{array}}$

Z

$\underline{\begin{array}{cc} \space \space \space \space 490_{10} \\ + 086_{10} \end{array}}$

576₁₀

Hence the result is 576