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Discrete vs continuous signal; convert (25.25)₁₀

Short answer

Continuous signals exist at all times with any amplitude; discrete signals are defined only at sampling instants. (25.25)₁₀ to binary: integer 11001, fraction .01 → 11001.01₂; to octal: integer 31, fraction .2 → 31.2₈.

Differentiate between discrete and continuous signal with necessary figures and example. Convert (25.25)₁₀ to binary and octal equivalent.

Discrete vs continuous signal

A continuous (analog) signal is defined at every instant of time and can take any value in a range. A discrete-time signal is defined only at specific (sampled) instants; if its values are also limited to fixed levels, it is a digital signal.

 Continuous x(t)          Discrete x[n]
    __                       |  |
   /  \      /             | |  | |
  /    \    /              | |  | |  |
 /      \__/            ---+-+--+-+--+--- n
---------------- t         0 1  2 3  4
Continuous signalDiscrete signal
Defined for all time ttDefined only at t=nTt = nT
Written x(t)x(t)Written x[n]x[n]
Example: voice, temperatureExample: daily rainfall, sampled audio
Processed by analog circuitsProcessed by digital systems

Convert (25.25)10(25.25)_{10} to binary

Integer: 25 → 25/2 = 12 r1, 12/2 = 6 r0, 6/2 = 3 r0, 3/2 = 1 r1, 1/2 = 0 r1 → 1100111001. Fraction: 0.25 × 2 = 0.5 → 0; 0.5 × 2 = 1.0 → 1 → .01.01.

Answer: (25.25)10=(11001.01)2(25.25)_{10} = (11001.01)_2

Convert (25.25)10(25.25)_{10} to octal

Integer: 25 ÷ 8 = 3 r 1; 3 ÷ 8 = 0 r 3 → 3131. Fraction: 0.25 × 8 = 2.0 → 2. (Check by grouping binary: 011 001 . 010 → 3 1 . 2.)

Answer: (25.25)10=(31.2)8(25.25)_{10} = (31.2)_8

✓ Answer checked by Claude Opus 5.5 (high effort)

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