You are recording a friend's 3-minute song with 24 bits per sample at 96 kHz sampling rate for a 5.1 surround sound system (6 channels). How much space will you save by recording this song with 16-bit, 44.1 kHz sampling for a stereo + subwoofer system (3 channels)? Note that you are making these recordings without using any compression. Please give you answer in terms of Gibibits and round to the nearest hundredth.

save space = 1.9626 Gibibits

Explanation:

given data

recording song time = 3 minute = 180 seconds

song per sample =  24 bits per sample

frequency = 96 kHz

surround sound system = 5.1

solution

first we get here required space for 24 bits at  96 kHz that is

required space = 24 × 96 × 10³ × 6 × 180

required space = 2.48832 ×  bits

as 1 Gib bit = bits

so required space = 2.48832 ×  bits ÷   bits

required space = 2.3174 Gibibits   ...............1

and

space required to save record 16 bit at 44.1 kHz

space required = 16 × 44.1 × 10³ × 3 × 180

space required = 0.381024 ×  bits

space required = 0.381024 ×  bits  ÷   bits  

space required = 0.3548 Gibibits    ...........2

so

we get here that save space in 16 bit at 44.1 kHz

save space = 2.3174 Gibibit - 0.3548 Gibibits

save space = 1.9626 Gibibits

answer:

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