Question

dfsc 2316 : pre - quiz 50 points, due 11:59:59 pm, 09/14/2025
please submit a pdf file (either ms - word saved as pdf or print and work on paper followed by a scan to pdf) prior to the deadline. upload the file to blackboard and bring a printout of your solutions to class on monday. failing to complete either step will result in no points on this quiz.

question 1 (10 pt). please convert the following numbers in different bases into decimal (base 10).

• 101₂=
• 01011₂=
• 10111010₂=
• a2b₁₆=
• 123₈=

question 2 (10 pt). in a 6 - bit system, use sign/magnitude scheme, please

• represent 7 and - 7 in binary (base 2)
• perform binary addition in this scheme
• check if the resulting sum is zero in decimal (base 10).

Explanation:

Step1: Convert $101_2$ to decimal

Use the formula $\sum_{i = 0}^{n - 1}a_i\times b^i$, where $b = 2$. So $1\times2^2+0\times2^1 + 1\times2^0=4 + 0+1=5$.

Step2: Convert $01011_2$ to decimal

$0\times2^4+1\times2^3+0\times2^2+1\times2^1+1\times2^0 = 0 + 8+0 + 2+1=11$.

Step3: Convert $10111010_2$ to decimal

$1\times2^7+0\times2^6+1\times2^5+1\times2^4+1\times2^3+0\times2^2+1\times2^1+0\times2^0=128 + 0+32+16+8+0 + 2+0 = 186$.

Step4: Convert $A2B_{16}$ to decimal

In hexadecimal, $A = 10$, $B=11$. So $10\times16^2+2\times16^1+11\times16^0=2560+32 + 11=2603$.

Step5: Convert $123_8$ to decimal

$1\times8^2+2\times8^1+3\times8^0=64+16 + 3=83$.

Step6: Represent 7 and - 7 in 6 - bit sign/magnitude binary

For 7, since it is positive, the left - most bit (sign bit) is 0. $7=0111_2$, padding with leading 0s to 6 bits gives $000111$. For - 7, the sign bit is 1, and the magnitude is $7 = 0111_2$, so it is $100111$.

Step7: Perform binary addition

$000111+100111 = 101110$.

Step8: Check the sum in decimal

$1\times2^5+0\times2^4+1\times2^3+1\times2^2+1\times2^1+0\times2^0=-32+0 + 8+4+2+0=-18
eq0$.

Answer:

$101_2 = 5$
$01011_2=11$
$10111010_2 = 186$
$A2B_{16}=2603$
$123_8 = 83$
7 in 6 - bit sign/magnitude: $000111$

• 7 in 6 - bit sign/magnitude: $100111$

Binary addition result: $101110$
Sum is not 0 in decimal.