The symbol £ is magnified and shown in Figure 1 with a grid superimposed. Figure 1 The image in Figure 1 is to be encoded and encrypted using the following steps: 1. Each of the five horizontal rows of the picture is encoded as a 5-bit binary number. White squares are encoded as Os and black squares as 1s. The horizontal rows are therefore encoded as: Row 1: 00110 Row 2: 01001 Row 3: 11100 Row 4: 01000 Row 5: 11110 2. Starting from the left, the first binary digit is multiplied by 16, the second by 8, the third by 4, the fourth by 2, and the fifth by 1. This will convert the 5-bit binary numbers to decimal numbers as shown below: Row 1: (0 x 16) + (0 × 8) + (1 × 4) + (1 × 2) + (0 × 1) = 0 + 0 +4+2+0= 6. 16) + (1 × 8) + (0 × 4) + (0 × 2) + (1 × 1) = 0 + 8 +0+0+1=9. Row 2: (0 x Row 3: (1 x 16) + (1 x 8) + (1 x 4) + (0 × 2) + (0 x 1) = 16 + 8 + 4 + 0 + 0 = 28. Row 4: (0 x 16) + (1 × 8) + (0 × 4) + (0 x 2) + (0 × 1) = 0 + 8 +0+0+0 = 8. Row 5: (1 x 16) + (1 × 8) + (1 × 4) + (1 × 2) + (0 × 1) = 16 + 8 +4+2+0 = 30. 3. The decimal number representing each row is encrypted using modular addition with a modulus of 32 and a key of 19. 4. The result of each row is converted to a 5-bit binary number. Use Steps 1 to 4 to work out the 5-bit binary number of each row. Show your working.
The symbol £ is magnified and shown in Figure 1 with a grid superimposed. Figure 1 The image in Figure 1 is to be encoded and encrypted using the following steps: 1. Each of the five horizontal rows of the picture is encoded as a 5-bit binary number. White squares are encoded as Os and black squares as 1s. The horizontal rows are therefore encoded as: Row 1: 00110 Row 2: 01001 Row 3: 11100 Row 4: 01000 Row 5: 11110 2. Starting from the left, the first binary digit is multiplied by 16, the second by 8, the third by 4, the fourth by 2, and the fifth by 1. This will convert the 5-bit binary numbers to decimal numbers as shown below: Row 1: (0 x 16) + (0 × 8) + (1 × 4) + (1 × 2) + (0 × 1) = 0 + 0 +4+2+0= 6. 16) + (1 × 8) + (0 × 4) + (0 × 2) + (1 × 1) = 0 + 8 +0+0+1=9. Row 2: (0 x Row 3: (1 x 16) + (1 x 8) + (1 x 4) + (0 × 2) + (0 x 1) = 16 + 8 + 4 + 0 + 0 = 28. Row 4: (0 x 16) + (1 × 8) + (0 × 4) + (0 x 2) + (0 × 1) = 0 + 8 +0+0+0 = 8. Row 5: (1 x 16) + (1 × 8) + (1 × 4) + (1 × 2) + (0 × 1) = 16 + 8 +4+2+0 = 30. 3. The decimal number representing each row is encrypted using modular addition with a modulus of 32 and a key of 19. 4. The result of each row is converted to a 5-bit binary number. Use Steps 1 to 4 to work out the 5-bit binary number of each row. Show your working.
Chapter7: Input/output Technology
Section: Chapter Questions
Problem 5VE
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Transcribed Image Text:The symbol £ is magnified and shown in Figure 1 with a grid superimposed.
Figure 1
The image in Figure 1 is to be encoded and encrypted using the following steps:
1. Each of the five horizontal rows of the picture is encoded as a 5-bit binary number. White squares are
encoded as Os and black squares as 1s. The horizontal rows are therefore encoded as:
Row 1: 00110
Row 2: 01001
Row 3: 11100
Row 4: 01000
Row 5: 11110
2. Starting from the left, the first binary digit is multiplied by 16, the second by 8, the third by 4, the fourth by 2,
and the fifth by 1. This will convert the 5-bit binary numbers to decimal numbers as shown below:
Row 1: (0 x 16) + (0 × 8) + (1 × 4) + (1 × 2) + (0 × 1) = 0 + 0 +4+2+0 = 6.
Row 2: (0 x 16) + (1 × 8) + (0 × 4) + (0 × 2) + (1 × 1) = 0 + 8 +0+0+1 = 9.
Row 3: (1 x 16) + (1 × 8) + (1 × 4) + (0 × 2) + (0 × 1) = 16+8+4 + 0 + 0 = 28.
Row 4: (0 x 16) + (1 × 8) + (0 × 4) + (0 × 2) + (0 × 1) = 0 + 8 +0+0+0= 8.
Row 5: (1 x 16) + (1 × 8) + (1 × 4) + (1 × 2) + (0 × 1) = 16 +8+4+2+0 = 30.
3. The decimal number representing each row is encrypted using modular addition with a modulus of 32 and a
key of 19.
4. The result of each row is converted to a 5-bit binary number.
Use Steps 1 to 4 to work out the 5-bit binary number of each row. Show your working.
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