Digital Systems T3 Flashcards
Assuming enough resources (2-input AND gates) are available, ALL partial products (PPs) are calculated
Concurrently
In a binary multiplication, which bits of the final product are calculated first?
The LSbits
Binary multiplication can be implemented in custom hardware (HW) or software (SW)
True
When is the value of the PP zero?
When the associated multiplier bit is 0
The most time-consuming operation in a binary multiplication is
The multi-operand addition of the PPs
In the SSRM discussed in class, PH-Reg is initiated to
0
in the SSRM discussed in class, the M-reg stores the value
Of the original multiplicand
In the SSRM described in class, a new PP is generated using
2-to-1 muxes
In the SSRM discussed in class, which sequence of operations are repeated?
Add shift-right
The SSRM mPL-Reg is used to store
The remaining bits of the multiplier and the incoming LSbits of the FP
The behavioral description of the SSRM SU uses if-else and/or case constructions. which of the following is NOT used in the condition evaluations of these constructs
DONE
The SSRM CST captures ONLY sequential events
False
Why is it necessary to use external control inputs START?
So that the SSRM knows when a new set of input operands is valid and ready to be multiplied
If the Multiplicand is n-bits wide and the multiplier is m-bits where how many times does the add-shift sequence repeat in the SSRM
m
In the lecture SSRM ASM chart we initialized n = 4 and counted down to 0. We would initialize n = 0, and we would need to
Count up to 4
How many different data sets can the PSRM be described in the class process concurrently?
4
The PSRM improves
Throughput
In each stage of the PSRM which operations are executed during every machine cycle
Add and shift right
In each PSRM stage, the PP is generated
using 2-input AND gates
On average, division takes longer than multiplication
True
The generate function indicates that a carry-out of ‘1’ will be generated by stage:
No matter what the carry-in value is
Compared to the RCA, a CLA uses:
More hardware resources
What is the RCA’s biggest performance problem?
The propitiation of carry values form one stage to the next
How many gate-level propagation delays are there in a generic SUM-Of-Producs (SOP)?
2
The propagate function p = ‘1’ the the carry-out value will be ‘1’ if:
The carry value is ‘1’
At the cost of additional and acceptable propagation delay, the second level carry-look-ahead reuses computation results in the form of
Gj, and Pj
In an attempt to trade odd code/performance, we can combine carry look-ahead and ripple-carry in the same adder unit
True
What is a practical limit for the number of inputs to a (static) CMOS gate?
4
How many gate-level propagation delays does it take to compute the sum of a stage in a RCA or CLA from the moment the cin to the stage is available
1
Comparing a n-bit CLA to a n-bit RCA:
The CLA is faster, bit uses significantly more hardware resources
In a positional number system, the position of a digit:
Represents the weight it carries
To convert a number to an IEEE floating point format, the number is first normalized. the integer part of the normalized value:
Is not stored, but implied when the value of the number is being reconstructed
In the IEEE floating formats, the stored exponent is stored in an excess form. this means that the actual exponent value is equal to:
The stored exponent value minus the excess value
To be able to use floating point numbers in manipulation, these have to be:
Unpacked -> Manipulated -> Packed
In a weighted number system, the value of a number is equal to:
The SUM of the PRODUCTS between each digit vale and the radix(or base) raised to the power of its position
Which representation covers a wider range of numbers?
Floating-Point
When the exponent = 111…1 and the fraction = 000…0 the number is interpreted as:
± infinity
The value 0 is represented by
Exponent = 0 and fraction (stored mantissa) = 0
When two floating point numbers are multiplied
The (1+ mantissas) are multiplied, and the exponents added
For addition and subtraction, the mantissas of floating point numbers
Have to be aligned
