Problem 8 (6 points) In Figure 3.15, for each of the two control signals to choo
ID: 3674611 • Letter: P
Question
Problem 8 (6 points) In Figure 3.15, for each of the two control signals to choose either 0 or 1 in the lower half of the diagram, based on the algorithm given in Figure 3.14, give the conditions when 0 is chosen and when 1 is chosen. You need to state clearly the conditions for the left and the right one respectively.
3.5 Floating Point 207 Exponent Fraction Sign Exponent Fraction Small ALU Compare exponents Exponent difference Shift smaller Control Shift right number right Add Big ALU 0 Increment or I decrement shift left or right Normalize Round Rounding hardware Fraction Sign Exponent FIGURE 3.15 Block diagram of an arithmetic unit dedicated to floating-point addition. The steps of Figure 3.14 correspond o each block, from top to bottom. First, the exponent of one operand is subtracted from the other using the small ALU to determine which is larger and by how much. This difference controls the three multiplexors; from left to right, they select the larger exponent, the significand of the smaller number, and the significand of the larger number. The smaller significand is shifted right, and then the significands are added together using the big ALU. The normalization step then shifts the sum left or right and increments or decrements the exponent. Rounding then creates the final result, which may require normalizing again to produce the actual final result.Explanation / Answer
From algorithm 3.14, if the sum is not normalized, it is needed to shift right or left and increment or decrement the exponent.
Now, in diagram 3.15,
1) Multiplexor on the right hand side receives the sum as the result of the addition of two significands.
a) 0 is chosen if the sum is recieved for the first time, after addition.
b) 1 is chosen if the sum is received subsequenty after first time, when the sum is still not normalized after shifting left or right and rounding.
2) Multiplexor on the left hand side receives the exponent of the larger number, which will also be the exponent of the sum as a result.
a) 0 is chosen, if exponent is received for the first time, before normalizing the sum.
b) 1 is chosen if the exponent if received subsequently after first time,when the exponent has been incremented or decremented and the result sum still does not seems to be normalized.