MATH SOLVE

3 months ago

Q:
# Determine the value of base b if (152)b = 0x6A. Please show all steps.

Accepted Solution

A:

Assuming 0x6A is given in base 16, first convert [tex]152_b[/tex] and [tex]6A_{16}[/tex] to a common base, say base 10:[tex]152_b=1\cdot b^2+5\cdot b^1+2\cdot b^0=(b^2+5b+2)_{10}[/tex][tex]6A_{16}=6\cdot16^1+10\cdot16^0=106_{10}[/tex]Then[tex]b^2+5b+2=106[/tex][tex]b^2+5b-104=(b-13)(b+8)=0[/tex][tex]\implies b=13[/tex]