Assignment 6: Arithmetic Operations
Due Date: Apr. 19, 2016
1. Consider the following decimal numbers (20 pts)
15.8125
293975.0125
1) Write down the binary representation of the decimal number, assuming the IEE 754 single precision
format.
2) Write down the binary representation of the decimal number, assuming the IEE 754 double precision
format.
2. In a von Neumann architecture, groups of bits have no intrinsic meanings by themselves. What a bit
pattern represents depends entirely on how it is used. Consider the following bit patterns expressed in
hexadecimal notation. (20 pts)
8D28000016
1) What decimal number does the bit pattern represent if it is an integer?
2) What decimal number does the bit pattern represent if it is an unsigned integer?
3) If the bit pattern is in an instruction register, what MIPS instruction will be executed?
4) What decimal number does the bit pattern represent if it is a floating point number? Use the IEEE 754
standard.
3. Assume
A = 50, B = 10
1) Using a table similar to that shown in Figure 3.7, calculate the product of unsigned 6-bit A and B, i.e.,
A*B, using the first version multiplication hardware described in Figure 3.4. (30 pts)
Step
0
Action
Initial Vals
Multiplier
001010
Multiplicand
000000110010
Product
000000000000
2) Using a table similar to that shown in Figure 3.11, calculate the division of unsigned 6-bit A and B, i.e.,
A/B, using the first version division hardware described in Figure 3.9. (30 pts)
Step
0
Action
Initial Vals
Quotient
000000
Divisor
001010000000
Remainder
000000110010