(a) Hexadecimal numbers are numbers in base 16. They use the following sixteen
digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F. They are
widely used in com-
puting, for example, to represent colors or network addresses of
computers.
i. Convert A2F1316 to decimal. Show your work.
ii. Convert 456710 into hexadecimal. Show your work.
iii. Convert 00010101100011002 to hexadecimal. Explain how can you
use
the fact that 16 = 24
?
iv. If you convert a 64-bit binary number into hexadecimal, how many hexadecimal digits does it have? Explain.
i) => A2F13 => Ax16^4+2x16^3+Fx16^2+1x16^1+3x16^0 => Ax65536+2x4096+Fx256+1x16+3x1 => 10x65536+2x4096+15x256+1x16+3x1 => 667411 Answer: 667411 ii) Divide 4567 successively by 16 until the quotient is 0 4567/16 = 285, remainder is 7 285/16 = 17, remainder is 13 17/16 = 1, remainder is 1 1/16 = 0, remainder is 1 Read remainders from the bottom to top as 11D7 Answer: 0x11D7 iii) Hexadecimal Binary 0 0000 1 0001 2 0010 3 0011 4 0100 5 0101 6 0110 7 0111 8 1000 9 1001 A 1010 B 1011 C 1100 D 1101 E 1110 F 1111 Use this table to convert from binary to hexadecimal Converting 0001010110001100 to hexadecimal 0001 => 1 0101 => 5 1000 => 8 1100 => C So, in hexadecimal 0001010110001100 is 0x158C Answer: 0x158C iv) each 4-bit binary is converted to a single symbol of hexadecimal so, 64-bits binary is converted to 64/4 = 16 digits of hexadecimal Answer: 16
(a) Hexadecimal numbers are numbers in base 16. They use the following sixteen digits: 0, 1,...
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