What decimal no. is represented by the binary number 111.111 ?


1 1 1 . 1   1    1
4 2 1   0.5 0.25 0.125

1 x 0.125 = 0.125
1 x 0.25  = 0.25
1 x 0.5   = 0.5

1 x 1     = 1
1 x 2	  = 2
1 x 4     = 4      +
            -------
            7.875 

What decimal no. is represented by the binary number 1111111 ?

Binary Decimal
1   =  1
10  =  2
100 =  4
1000 = 8
10000= 16
100000= 32
1000000= 64
10000000= 128

 1111111 = 127
       1+
 -------
10000000

We did (2^7) - 1
2^7= 128 
128-1 = 127

------

 00
 01
 10
 11  3
100 (4-1)

-----

 000
 001
 010
 011
 100
 101
 110
 111
1000 = (8-1)= 7

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What decimal no. is represented by the octal no. 
123.7 ?

 1  2 3 . 7
64  8 1   1/8

7 x 1/8 = 7 * 0.125 = 0.875
3 x 1   =             3
2 x 8   =            16
1 x 64  =            64     +
                    -------- 
                     83.875

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What decimal no. is represented by the hexadecimal no.?
A10.4 ?

A      1  0 . 4
256   16  1   1/16


4 x 1/16 = 4 * 0.0625 = 0.25
0 x 1    =              0
1 x 16   =             16
A(10) x 256 =        2560    +
                     --------
                     2576.25

Base 7
------
100 (base 7) = 49

 1 0 0
49 7 1

Question
--------
Convert the decimal no. 128.75 to binary?

128 - divide by 2 repeatedly. Gather your remainders

128 / 2 = 64 r 0
64 /2 =   32 r 0
32 /2 =   16 r 0
16 /2 =    8 r 0
8  /2 =    4 r 0
4  /2 =    2 r 0
2  /2 =    1 r 0
1  /2 =    0 r 1   (up) 10000000

.75 x 2 = (1).5    (down)
.5  x 2 = (1).0
0

10000000.11

------
.75 x 2 = (1)  .5
.5  x 2 = (1)  .0
.0

------

.625 x 2 = (1) .25   (read down)
.25  x 2 = (0) .5
.5   x 2 = (1) .0
.0

Decimal= Binary
 .625 =   .101
0.625 =  0.101

------

Convert 8.125 (decimal) to binary.

8/2 = 4 r 0
4/2 = 2 r 0
2/2 = 1 r 0
1/2 = 0 r 1  (read up) 1000

.125 x 2 = (0) .25 (read down for fractional part)
.25  x 2 = (0) .5
.5   x 2 = (1) .0
.0

(0)(0)(1)

Decimal Binary
8.125 = 1000.001