Can you please explain step by step on how to do each of these two problems below? And then tell me whether it involves an arithmetic sequence or a geometric sequence I also need to show the work on both problems thank you.
Perform the indicated operations
1010 two × 101 two
A25 sixteen × 4 sixteen
http://en.wikipedia.org/wiki/Binary_numeral_system
IN this, it is easy by shifting registers, one of the great advantages of binary.
1010 x 101= 1010+101000 and add
110010 (check the add, I did it in my head.)
a25x
base 16
a25
x 4
________________
4x5 = 20= 16+4 or 14
4x2=8
4xA=40=2x16+8 or 28
now add
2800
++80plus signs are inserted to line up
++14
____
total 2894 check that.
http://www.csgnetwork.com/hexmultdivcalc.html
Sure! Let's go through each problem step by step and determine whether it involves an arithmetic sequence or a geometric sequence.
1. 1010 two × 101 two
To multiply two numbers in binary, you can use the same method as multiplying in decimal. Each digit in the binary number represents a power of 2. Here's how you can perform the multiplication:
Step 1: Write down the given numbers vertically.
1010 two
× 101 two
------------
Step 2: Start multiplying from the rightmost digit of the bottom number.
Multiply 0 by 1010 two:
0
x1010 two
------------
00000 two
Step 3: Multiply the next digit in the bottom number, which is 1, by the top number shifted one digit to the left.
Multiply 1 by 1010 two:
1
x1010 two
------------
1010 two
Step 4: Add the partial products:
1010 two
+ 00000 two
------------
1010 two
The final result is 1010 two, which is equivalent to the decimal number 10. Since the numbers in this problem are binary, it doesn't involve an arithmetic or geometric sequence.
2. A25 sixteen × 4 sixteen
To multiply two numbers in hexadecimal (base 16), you can also use a similar method as multiplying in decimal. Each digit in hexadecimal represents a power of 16. Let's go through the steps:
Step 1: Write down the given numbers vertically.
A25 sixteen
× 4 sixteen
--------------
Step 2: Start multiplying from the rightmost digit of the bottom number.
Multiply 4 by A25 sixteen:
4
xA25 sixteen
--------------
14
46A0
--------------
Step 3: Multiply the next digit in the bottom number, which is 0, by the top number shifted one digit to the left.
Multiply 0 by A25 sixteen:
0
xA25 sixteen
--------------
0
0
--------------
Step 4: Multiply the next digit in the bottom number, which is 0, by the top number shifted two digits to the left.
Multiply 0 by A25 sixteen:
0
xA25 sixteen
--------------
0
0
0
--------------
Step 5: Add the partial products:
14
+ 46A0
--------------
46B4
The final result is 46B4 sixteen, which is equivalent to the decimal number 18004. Since the numbers in this problem are hexadecimal, it also doesn't involve an arithmetic or geometric sequence.
In both problems, there is no arithmetic or geometric sequence involved as they are simply multiplication operations in different number systems.