1. a. Fill in the table for the Quotient, Divisor and Dividend for each step. Yo
ID: 3847843 • Letter: 1
Question
1.
a. Fill in the table for the Quotient, Divisor and Dividend for each step. You need to provide the DESCRIPTION of the step being performed (shift left, shift right, sub). The value of Divisor is 4 (0100, with additional 0000 bits shown for right shift), Dividend is 6 (initially loaded into the Remainder).
Table headline Quotient Divisor Remainder Description Step#
b. What is the smallest positive (not including +0) representable number in 32-bit IEEE 754 single precision floating point? Show the bit encoding and the value in base 10 (fraction or decimal OK).
Explanation / Answer
1)
a)Answer
Quotient Divisor Remainder Description Steps
------------------------------------------------------------------------------------------ -----------------------
0000 0100 0000 0000 0110 Given Values Step 0
0000 0100 0000 1100 0110 Remainder = Remainder – Divisor Step 1
0000 0100 0000 0000 0110 Remainder < 0 => +Divisor , sll Q, Q0 = 0 Step 2
0000 0010 0000 0000 0110 Shift Divisor to right Step 3
0000 0010 0000 1110 0110 Remainder = Remainder – Divisor Step 4
0000 0010 0000 0000 0110 Remainder < 0 => +Divisor , sll Q, Q0 = 0 Step 5
0000 0001 0000 0000 0110 Shift Divisor to right Step 6
0000 0001 0000 1111 0110 Remainder = Remainder – Divisor Step 7
0000 0001 0000 0000 0110 Remainder < 0 => +Divisor , sll Q, Q0 = 0 Step 8
0000 0000 1000 0000 0110 Shift Divisor to right Step 9
0000 0000 1000 1111 1110 Remainder = Remainder – Divisor Step 10
0000 0000 1000 0000 0110 Remainder < 0 => +Divisor , sll Q, Q0 = 0 Step 11
0000 0000 0100 0000 0110 Shift Divisor to right Step 12
0000 0000 0100 0000 0010 Remainder = Remainder – Divisor Step 13
0001 0000 0100 0000 0010 Remainder > 0 => sll Q, Q0 = 1 Step 14
0001 0000 0010 0000 0010 Shift Divisor Right Step 15
b)Answer
The smallest positive (not including +0) representable number 32-bit IEEE 754 single precision floating point value is
0 00000000 00000000000000000000001
The decimal value is = (+1) * (2(0-127))*(1. 00000000000000000000001)
= 5.87747175411e-39.
Hope the answer will help you Thank you..
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