Digital Electronics Test 2

Concept:

Resolution is defined as the smallest change in the analog output voltage corresponding to a change of one bit in the digital output.

The percentage resolution of an n-bit DAC is given by:

\(\%R = \frac{1}{{{2^n} - 1}} × 100\)

Also, the full-scale output for the given step size (Δ) is given by:

V_FS = (2ⁿ - 1) × Δ

where 2ⁿ - 1 = Number of levels

Calculation:

Given Δ = 20 mV and n= 8.

The full-scale output will be:

VFS = (28 - 1) × 20 mV

V_FS = 5.1 V

also, the percentage resolution will be:

\(\%R = \frac{1}{{{2^8} - 1}} × 100\)

%R = 0.4 %

(P) X̅ Y̅ Z̅ + X̅ Y Z̅ + X̅ Y Z

= X̅ Y̅ Z̅ + X̅ Y̅ Z̅ + X̅ Y Z̅ + X̅ Y Z

= X̅ Z̅ (Y̅ + Y) + X̅ Y (Z̅ + Z)

= X̅ Z̅ + X̅ Y

= X̅ (Y + Z̅) = L

(Q) X Y Z + X Y̅ Z + X Y Z̅

= X Y Z + X Y̅ Z + X Y Z + X Y Z̅

= X Z (Y + Y̅) + X Y (Z + Z̅)

= XZ + X Y

= X (Y + Z) = K

(R) X Y + X Y Z + X Y Z̅ + X̅ Y Z

= XY (1 + Z + Z̅) + X̅ Y Z

= X Y + X̅ Y Z

= Y (X + X̅ Z) = Y (X + Z) = N

(S) X̅ Y̅ Z + X̅ Y Z + X Y̅ Z + X Y Z

= X̅ Z (Y̅ + Y) + XZ (Y̅ + Y)

= X̅ Z + X Z = Z (X̅ + X)

= Z = M