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 +
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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
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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
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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