Question

1. The unsigned decimal value (1,036)₁₀ is to be stored as a 16-bit word in memory.
   1. Show the 16-bit unsigned binary representation of (1,036)₁₀.
   2. Show the 4-digit unsigned hexadecimal representation of (1,036)₁₀.
   3. The unsigned binary value of part (a) should be stored using two bytes of a byte-addressable memory at locations 400 and 401. Specify the hexadecimal value in each byte for a “big endian” instruction set architecture. Give your answer by showing a table like the one below.

                                                                                               Big Endian

Location Contents (Byte) 400:

401:

Answer 1

a)
Divide 1036 successively by 2 until the quotient is 0
   > 1036/2 = 518, remainder is 0
   > 518/2 = 259, remainder is 0
   > 259/2 = 129, remainder is 1
   > 129/2 = 64, remainder is 1
   > 64/2 = 32, remainder is 0
   > 32/2 = 16, remainder is 0
   > 16/2 = 8, remainder is 0
   > 8/2 = 4, remainder is 0
   > 4/2 = 2, remainder is 0
   > 2/2 = 1, remainder is 0
   > 1/2 = 0, remainder is 1
Read remainders from the bottom to top as 10000001100
So, 1036 of decimal is 10000001100 in binary
so, 1036 in 16-bit binary is 0000010000001100
Answer: 0000010000001100

b)
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 0000010000001100 to hexadecimal
0000 => 0
0100 => 4
0000 => 0
1100 => C
So, in hexadecimal 0000010000001100 is 0x040C
Answer: 0x040C

c)
using big-endian
0x04 is stored at memory location 400
0x0C is stored at memory location 401
Answer:
---------
400:    0x04
401:    0x0C