國立暨南國際大學 97 學年度第一學期小考試卷

(考試時間: 14:10-14:40)

1. (10%) In contrast to a binary numbering system which has only two digits 0 and 1, a "septenary" system has only seven digits 0, 1, 2, 3, 4, 5, 6. In this system, 10₇ = 7₁₀, and 11₇ = 8₁₀.
   Convert the following septenary numbers to their corresponding hexadecimal representation.
   1. 12₇
   2. 34₇
   3. 56₇
   4. 22₇
   5. 25₇
      
      
2. (10%) Perform the following operations in septenary systems and write down the result (also in septenary systems).
1. 12₇ + 34₇
2. 56₇ + 56₇
3. 11₇ * 11₇
4. 12₇ * 12₇
5. 25₇ * 25₇
   
   
3. (10%) Perform the following operations in hexidecimal systems and write down the result (also in hexidecimal systems).
   1. 0x8 + 0x8
   2. 0x10 + 0x10
   3. 0x11 * 0x11
   4. 0x16 * 0x16
   5. 0x22 - 0x19
      
      
4. (10%) Using 4-bit allocation, interpret 1001 if the number was stored as
1. unsigned integer
2. sign-and-magnitude
3. one's complement
4. two's complement
5. Excess_7
   
   
5. (10%) Transform the fraction 0.14159 to a binary of 6 bits.
   
   
   
   
   
6. (10%) Represent 3.140625 in 32-bit IEEE format.
   Hint: The 32-bit IEEE format uses 1 bit to indicate the sign, 8 bits to store the exponent (in Excess_127 format), and 23 bits for mantissa.