Spring 2019 EE380 Assignment 4 Solution

This MIPS/SPIM program includes a subroutine called myadd that performs x=(y+z);. In the space below, replace the myadd subroutine with one named posfmin that will make x = min(y,z) where x, y, and z are all positive normal floating-point numbers (not negative, not denormals, and not NaN nor Inf). Although these are all floating-point values, you only may use the MIPS integer instructions that we have discussed -- no MIPS floating-point instructions are allowed here.

#### # # Integer less than comparison works for positive floats # # x = min(y, z) # .text .globl posfmin posfmin: la $t0, y # t0 = y lw $t0, 0($t0) la $t1, z # t1 = z lw $t1, 0($t1) slt $t2, $t0, $t1 # integer y<z bne $t2, $0, skip or $t0, $t1, $t1 skip: la $t2, x # x = t0 sw $t0, 0($t2) jr $ra # return
For this question, check all that apply. We discussed a variety of methods for performing binary addition. Which of the following ststements are true?
Ripple Carry uses less circuitry than other methods
Speculative Carry is always faster than carry select
Carry Lookahead computes the carry for the Nth bit position in O(log N) time
Carry Select implements K-bit addition using simultaneous (K/2)-bit additions
Speculative Carry implements K-bit addition using simultaneous (K/2)-bit additions
You know that to multiply a binary integer by 16, all you have to do is shift the value over by 4 bit positions -- which in hardware can literally be done without a function unit simply by connecting bus wires such that bit k goes to position k+4 and positions 0-3 are connected to ground. Well, it's harder to multiply by 28. However, by using Booth's algorithm, a single 32-bit add/subtract ALU is sufficient to implement multiply of a 32-bit number by 28 as a fast combinatorial circuit. Explain how this would be done by giving a formula for X*28 as a C expression (for example, X*5 would be (X<<2)+X).
X*28 = X*16 + X*8 + X*4 X*28 = X*32 - X*4 = (X<<5) - (X<<2)
For this question, check all that apply. In mathematics, both addition and multiplication are associative; for example, a*(b*c) gives the same value as (a*b)*c. Assuming no values go out of range, are addition and multiplication are associative for 2's complement binary integers and for IEEE-format floating-point values? Mark all the operations that are associative.
32-bit integer addition
32-bit (single) floating-point addition
64-bit (double) floating-point addition
32-bit (single) floating-point multiplication
64-bit (double) floating-point multiplication
For this question, check all that apply. In the single-cycle design shown in the above (rather large and very familiar) figure, which of the following signals are "don't cares" when executing a MIPS sw instruction?
Branch
must be 0
RegDst
ALUSrc
must be 1
RegWrite
must be 0
MemWrite
must be 1
For this question, check all that apply. In the single-cycle design shown in the above (rather large and very familiar) figure, suppose that ALUSrc=0 and RegWrite=1. Which of the following MIPS instructions might be executing?
sw $t0,4($t1)
ALUSrc=1, RegWrite=0
lw $t0,4($t1)
ALUSrc=1, RegWrite=1
beq $t0,$t1,l
ALUSrc=0, RegWrite=0
andi $t0,$t1,2
ALUSrc=1, RegWrite=1
add $t0,$t1,$t2
What is the logic formula for Y?

Y = OR(AND(A, B), AND(NOT(A), NOT(B), NOT(C)))
When determining the bit patterns to be used to represent instructions (or control signals in a circuit), one can use either horizontal or vertical encoding. Briefly describe one reason to prefer an encoding that is horizontal and one reason to prefer a vertical encoding.
Horizontal: no decoding overhead, allows VLIW-like packing Vertical: uses fewer bits; smaller instructions, less bandwidth

Computer Organization and Design.