Before tackling this question you should study Block 2 Parts 5 and 6.

a.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:

Each of the five horizontal rows of the picture is encoded as a 5-bit binary number. White squares are encoded as 0s 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

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 16) + (0 8) + (1 4) + (1 2) + (0 1) = 0 + 0 + 4 + 2 + 0 = 6.

Row 2: (0 16) + (1 8) + (0 4) + (0 2) + (1 1) = 0 + 8 + 0 + 0 + 1 = 9.

Row 3: (1 16) + (1 8) + (1 4) + (0 2) + (0 1) = 16 + 8 + 4 + 0 + 0 = 28.

Row 4: (0 16) + (1 8) + (0 4) + (0 2) + (0 1) = 0 + 8 + 0 + 0 + 0 = 8.

Row 5: (1 16) + (1 8) + (1 4) + (1 2) + (0 1) = 16 + 8 + 4 + 2 + 0 = 30.

The decimal number representing each row is encrypted using modular addition with a modulus of 32 and a key of 19.

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.

(3 marks)