Question

Solve for y in the equation; y/y+101 = 11/10010 all in base 2​

Answer 1

y = 1

Explanation:

We convert the numbers from the binary system to a decimal system:

`101_2=1\cdot2^2+0\cdot2^1+1\cdot2^0=4+0+1=5_(10)\\\\11_2=1\cdot2^1+1\cdot2^0=2+1=3_(10)\\\\10010_2=1\cdot2^4+0\cdot2^3+0\cdot2^2+1\cdot2^1+0\cdot2^0=16+0+0+2+0=18_(10)`

Therefore we have

`(y_2)/(y_2+101_2)=(11_2)/(10010_2)\Rightarrow(y)/(y+5)=(3)/(18)\qquad\text{cross multiply}\\\\18y=3(y+5)\qquad\text{use the distributive property}\\\\18y=3y+15\qquad\text{subreact}\ 3y\ \text{from both sides}\\\\15y=15\qquad\text{divide both sides by 15}\\\\y=1_(10)\Rightarrow y_2=1\cdot2^0=1_2`