Fall 2012
Computer Organization and Architecture
Set No 1. Representation of the information
1. Given a fixed decimal point representation in base 10, with 3 digits for the integer part and 3 digits
for the fractional part: XXX.YYY
a) What is the range of the number? (Compute the largest positive and negative number)
b) What is its precision? (Compute the difference between two consecutive numbers.
Remember that error is ½ of the precision)
2. Convert the following numbers using the least amount of digits:
a) (47)10 to signed binary.
b) (-27)10 to signed and binary magnitude
c) (213)16 to a 10 base number
d) (10110.101)2 to a 10 base number
e) (34.625)10 to a 4 base number
3. Convert the following numbers using the least amount of digits.
a) (011011)2 to a 10 base number
b) (-27)10 to excess binary 32 >> add to the original number, 32: N' = N + 32
c) (011011)2 to 16 base number
d) (55.875)10 to unsigned binary
e) (132.2)4 to 16 base number
4. Convert (0.201)3 to decimal.
5. Represent (43.3)7 as a 8 base using only one integer digit. Truncate the rest. Use a numerical
unsigned representation.
6. Find the decimal equivalent for the following 4-bits number expressed in C-2 1000.
7. Find the decimal equivalent for the following 4-bits number expressed in C-1 1111
8. Display the following number (305)10 using BCD.
9. Complete the following table for a 5-bit representation (including the sign bit). Show results as 10
base with sign integers.
Sign and magnitude 5 bits 5 bits excess 16
Largest number
Largest negative number
Amount of different numbers
10. IBM's floating point representation uses a 16 base, a sign bit, a 7 bi exponent expressed in excess-64
and a normalized binary mantissa of 24 bits .
a) ¿What number is represented in the following pattern??
1 0111111 01110000 00000000 00000000
Show your answer in decimal. The spaces are for an easier reading of the number
b) Represent the following number (14.3)10 using this notation
15. Represent the following number (107.15)10 as floating point with a sign bit, exponent as 7 bit excess-
64 and a normalizad magnitude in 24 bit. No hidden bit. Truncate the fraction part if necessary.
16. For the following pattern in IEEE 754 as single precisión, show the numeric value. (ex 1.11 x 25).
a) 0 10000011 01100000000000000000000
b) 1 10000000 00000000000000000000000
c) 1 00000000 00000000000000000000000
