binary notation

Question

. Represent the following number in binary notation:
a) 64
b) 192
c) 348
d) 2121
e) 741

Answer 1

For each number, do repeated divisions by 2 collecting the remainders in an ordered list. When done the reverse ordered remainders constitute the number in binary.

I’ll do a couple of the numbers to give you the idea; you do the others. "_10" and "_2" mean base 10 and 2 respectively.

c)

348
174 0
87 0
43 1
21 1
10 1
5 0
2 1
1 0
0 1

348_10 = 101011100_2

d)

2121
1060 1
530 0
265 0
132 1
66 0
33 0
16 1
8 0
4 0
2 0
1 0
0 1

2121_10 = 100001001001_2

Answer 2

Binary notation, also known as base two is the numbering system of computers. Basically instead of using 10 digits (0-9) to represent numbers you use only two digits, 0 and 1, and instead of having a 10s place and 100s place you have a twos place, a fours place, an eights place etc.

 

To transform a decimal number into a binary number you keep dividing by two, keeping track of the remainder until you can't.

 

So to start with 64:

 

64 / 2 = 32 and the remainder is 0

32 / 2 = 16 and the remainder is 0

16 / 2 =  8 and the remainder is 0

8 / 2   =  4 and the remainder is 0

4 / 2   =  2 and the remainder is 0

2 / 2   =  1 and the remainder is 0

1 / 2   =  0 and the remainder is 1

 

Walk it backwards and the binary notation of 64 is 1000000

 

192:

 

192 / 2 = 96 r 0

 96 / 2 = 48 r 0

 48 / 2 = 24 r 0

 24 / 2 = 12 r 0

 12 / 2 = 6 r 0

   6 / 2 = 3 r 0

   3 / 2 = 1 r 1

   1 / 2 = 0 r 1

 

192 = 11000000

 

348:

 

348 /2 = 174 r 0

174 /2 = 87 r 0

  87 /2 = 43 r 1

  43 /2 = 21 r 1

  21 /2 = 10 r 1

  10 /2 = 5 r 0

    5 /2 = 2 r 1

    2 /2 = 1 r 0

    1 /2 = 0 r 1

 

348 = 101011100

 

Following the same logic 2121 = 100001001001 and 741 = 1011100101

 

Answer 3

Binary notation uses only zero & one, but place value determines their actual value. The first place has a value of one, the second place has a value of two, and each place after that is double the value of the previous place (1,2,4,8,16,32,64,etc.).

Thus, 1=1 & 10=2 (2+0).

a) 64 is the 7th place, so a 1 goes in the 7th place, followed by zeros: 1000000;

b) 192 is 128+64, so 1 goes in the 8th & 7th places, followed by zeros: 11000000;

c) 348 is 256+64+16+8+4, so we write 101011100. There are no 128, 32, 2, or 1, so we hold those places with zeros;

d) 2121 is 2048+64+8+1, so we write 100001001001. 2048 is the 12th place;

e) 741 is 512+128+64+32+4+1, so we write 1011100101.

Make a place value chart, practice, think carefully, and check your work against the chart - always make sure you write the correct number of places - you'll get the hang of it!