यदि `(10x 010)_(2) - (11y1)_(2) = (10 z 11)_(2)` हो , तो द्वि - आधारी अंकों `x , y , z` के सम्भावित मान क्रमश: क्या है ?

Options

A. `0,0,1`
B. `0,1,0`
C. `1,1,0`
D. `0,0,0`

Answer

B

Explanation

`(10x 010)_(2) - (11y1)_(2) = (10z 11)_(2)`
`implies (2^(5) xx 1 + 0+ 2^(3) xx x + 0 xx 2^(2) + 1 xx 2^(1) + 0 xx 2^(0)) - (2^(3) xx 1 + 2^(2) xx 1 + y xx 2^(1) + 1 xx 2^(0))`
`= 2^(4) xx 1 + 0 + 2^(2) xx z + 2^(1) xx 1 + 2^(0) xx 1 `
`implies (34 + 8x) - (13 + 2y) = 19 + 4z`
`implies 2 = - 8 x + 2y + 4z`
`implies x = 0 , y = 1 , z = 0`