Data Representation

Question 1

Convert the following numbers from hexadecimal to binary and to decimal

0x3F
0xDE

Answer 1

Answer:

Hexa: 0x3F
Binary: 0011111

Hexa: 0xDE
Binary: 11011110

Question 2

Complete the following table, converting the binary numbers to decimal and decimal numbers to binary.

Binary to Decimal
11001110
01010101

Decimal to Binary
37
85

Answer 2

Answer:

Binary to Decimal
11001110    =>   128 + 64 + 8 + 4 + 2 => 206
01010101 => 0x55 (another approach)
(5 x 16^1) + (5 x 16^0) = 80 + 5 = 85
alternatively, 
64 + 16 + 4 + 1 = 85

Decimal to Binary
37 
=> (37/2)  a: 18 r: 1
=> (18/2)   a: 9 r: 0
=> (9/2)    a: 4 r: 1
=> (4/2)    a: 2 r: 0
=> (2/2)    a: 1  r: 0
=> (1/2)     a: 0 r: 1
=> 00100101

alternatively, 
85 
=> (85/16) a: 5 r: 5
=> (5/16)   a: 0 r: 5
=> 0x55 => 01010101

Question 3

Write an octal number which has the hexadecimal value 0xA6D.

Answer 3

Answer:

Hex to Binary to Octal
0xA6D => 1010 01101101 => 101 001 101 101

Octal: 5155 (base 8)

Question 4

Consider the following declarations in the C language:

char x = -98;
unsigned char y = (unsigned char) x;

What is the decimal value of y?

Answer 4

Answer: y = 158

98 (unsigned) is 0x 62 => 01100010
2’s complement = 10011101 +1 => 10011110
=> 128 + 16 + 14 = 158