Computer Architecture: More exercises on Data Representation

1. The binary representation of the hexadecimal number (3B7F)16   is (choose one):

(A) 0100 1001 1110 1101 (B) 0011 1011 0111 1111 (C) 0010 0100 0000 1010
(D) 0110 0011 1011 1100 (E) 1101 1100 1011 0101

2. Convert the following numbers as indicated.

(a) (110101)2 to unsigned base 10.
(b) (−29)10 to two’s complement (use 8 bits in the result).
(c) (61543)8 to unsigned base 16 (use four base 16 digits in the result).
(d) (37)10 to unsigned base 3 (use four base 3 digits in the result).

3. A computer with a 32-bit word size uses two's complement to represent numbers. The range of integers that can be represented by this computer is:

(A) –232 to 232 (B) –231 to 232 (C) –231 to 231 – 1 (D) –232 to 23 (E) –232 – 1 to 232

4. Computer A uses the following 32-bit floating-point representation of real numbers:


Computer B uses the following floating point representation scheme:


Which of the following statements is true with regard to Computer B’s method of representing floating-point numbers over Computer A’s method?

(A) both the range and precision are increased
(B) the range is increased but the precision is decreased
(C) the range is decreased but the precision is increased
(D) both the range and precision are decreased
(E) both the range and precision remain the same

5. Express (-1/32)10 in the IEEE 754 single precision format.

6. Represent (107.875)10 in the IEEE-754 single precision floating point representation which has a sign bit, an eight-bit excess 127 exponent, and a normalized 23-bit significand in base 2 with a hidden 1 to the left of the radix point. Truncate the fraction if necessary by chopping bits as necessary.

7. Using a floating point representation with a sign bit in the leftmost position, followed by a three-bit excess 4 exponent, followed by a normalized six-bit fraction in base 4. Zero is represented by the bit pattern