Question

Question 3:

1. Perform a binary multiplication on the two following numbers:

(75)₁₀ X (6)₁₀

You must show all the steps of your work

2. Using BCD, add (10000101)₂ to (00110101)₂. Display the result in decimals.

You must show all the steps of your work

Answer 1

Q1) (75)₁₀ x (6)₁₀
Converting 75 and 6 to binary

2|75|1
2|37|1
2|18|0
2|9 |1
2|4 |0
2|2 |0
2|1 |1
|0 |

2|6|0
2|3|1
2|1|1
|0|

so (75)₁₀ = (1001011)₂ and (6)₁₀ is (110)₂

multiplicating

1001011
x 110
0000000
10010110
100101100
=111000010

111000010 in decimal is 450 and 75 x 6 is also 450

Q2
add (10000101)₂ and (00110101)₂ using BCD

1000 0101
+ 0011 0101
= 1011 1010
so 1011 and 1010 are greater than 9 so we add 6 that is 0110 to both the 4 bits

1011 1010
+0110 0110
=1 0010 0000
which is 0001 0010 0000 in binary and in decimal it is 120

1000 0101 in decimal is 85
8 5

and
0011 0101
3 5
so 85 + 35 is 120 which is shown by our calculations.