7.B] Given a grayscale image of size 5 inches by 6 inches scanned at the rate of 300 dpi, answer the following:
i) How many bits are required to represent the image?
ii) How much time is required to transmit the image if the modem is 28 kbps?
iii) Repeat the above calculations if it were a binary image.
Answer:
Given:
- Image size: 5 inches by 6 inches
- Scanning rate: 300 dpi (dots per inch)
- Modem speed: 28 kbps (kilobits per second)
i) Number of Bits Required to Represent the Image (Grayscale Image)
- Calculate the Image Resolution:
- Width in pixels = 5 inches × 300 dpi = 1500 pixels
- Height in pixels = 6 inches × 300 dpi = 1800 pixels
- Determine the Number of Pixels:
- Total pixels = 1500 pixels × 1800 pixels = 2,700,000 pixels
- Bits per Pixel:
- A grayscale image typically uses 8 bits per pixel.
- Calculate Total Number of Bits:
- Total bits = Number of pixels × Bits per pixel
- Total bits = 2,700,000 pixels × 8 bits/pixel = 21,600,000 bits
ii) Time Required to Transmit the Image (Grayscale Image)
- Convert Modem Speed to Bits per Second:
- Modem speed = 28 kbps = 28,000 bits per second
- Calculate Transmission Time:
- Transmission time = Total bits / Modem speed
- Transmission time = 21,600,000 bits / 28,000 bits/second ≈ 771.43 seconds
iii) Repeat the Calculations for a Binary Image
- Bits per Pixel for Binary Image:
- A binary image uses 1 bit per pixel.
- Calculate Total Number of Bits:
- Total bits = Number of pixels × Bits per pixel
- Total bits = 2,700,000 pixels × 1 bit/pixel = 2,700,000 bits
- Calculate Transmission Time:
- Transmission time = Total bits / Modem speed
- Transmission time = 2,700,000 bits / 28,000 bits/second ≈ 96.43 seconds
Summary
For the Grayscale Image:
- Bits Required: 21,600,000 bits
- Transmission Time: 771.43 seconds
For the Binary Image:
- Bits Required: 2,700,000 bits
- Transmission Time: 96.43 seconds