a Give the representation of the decimal number 18 in hex ie

a. Give the representation of the decimal number 18 in hex (ie, hexadecimal base 16 notation).

b. Give the binary representation of the hexadecimal number 1F. do you see a relationship between the hex representation and the binary?

c. Give the decimal equivalent of the base 5 number 143.

Solution

a) The number 18 in hex is 12. The number can be represented in these two ways as 16*1+1*2 = 10*1+1*8.

b) 1F in binary is 11111. The relationship is not very evident in this example, the method is we use four bits to create each digit in hex. F is 15, so in binary it is 1111 and 1 in decimal is 0001. So the total number is 00011111.

c) The number 143 base 5 in decimal is 25*1+5*4+1*3 = 48.