Sunday, 9 February 2014

Binary conversions and logic operations

1a
00110111 = 32+16+4+2+1 = 55 
128
64
32
16
8
4
2
1
0
0
1
1
0
1
1
1
0
1
1
1
0
1
1
0
1
1
0
0
1
1
0
1
01110110 = 64+32+16+4+2 = 118
11001101 = 128+64+8+4+1 = 205
4
2
1
0
1
0
1
0
1
0
0
0
B
A8 = 10101000 = 010 101 000
                                     2      5    0   = 250

4E = 01001110 = 001 001 110
4
2
1
0
0
1
0
0
1
1
1
0
    1      1     6     = 116


BB = 10111011 = 010 111 011
4
2
1
0
1
0
1
1
1
0
1
1
                                    2      7      3       =273 



C
01110110 = +118
0=+/1=-
64
32
16
8
4
2
1
0
1
1
1
0
1
1
0
1
0
0
1
1
0
0
1
1
0
0
0
1
1
1
1

10011001 = -25

10001111 = -15

D
-128
64
32
16
8
4
2
1
1
0
0
0
1
1
1
0
1
0
1
1
1
0
0
1
1
1
0
0
1
1
1
1
10001110 = (-128) + 8+4+2 = -114
10111001 = (-128) + 32+16+8+1 = -71
11001111 = (-128) +64+8+4+2+1 =-49

E
121 = 64+32+4+1
-128
64
32
16
8
4
2
1
0
1
1
0
0
1
0
1
0
1
0
1
1
1
1
0
1
1
1
0
1
1
1
0
1
0
0
0
1
1
1
1
94 = 64+16+8+4+2
-18 = -128+64+32+8+4 = 00010010 =18
                                                11101101
                               LSB +1 = 11101110 = -18
-112 = -128+8+4+2 = 01110000 = 112
                                         10001111
                        LSB +1 = 10010000 = -112

F
n/a
s

m
m
m
m

e
e
e
n/a
+ve/-ve

8
4
2
1

4
2
1
8.5
0

1
0
0
0

1
0
0
-13.0
1

1
1
0
1

1
0
0
0.625
0

1
0
1
0

0
0
0
-0.3125
1

0
1
0
1

0
0
0
8.5                         
.5 x2 = 1

-13.0          
                    
0.625
.625 x2 =1.25
.25   x2 = 0.5
.5      x2 = 1
                               
-0.3125
0.3125 x2 = 0.625
0.625   x2 = 1.25
0.25     x2 = 0.5
0.5       x2 = 1



A
B
1
X=B  1
X+A
1
1
1
1
1
1
0
1
0
1
0
1
1
1
1
0
0
1
0
0
P4
A+B  1                                                              




A
B
C
output
1
1
1
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
 C





A
B
X
C
output
1
1
0
0
1
0
0
0
0
0
1
0
1
0
1
1
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0







B
C
X
A
Y=XA
A
Output=Y+A
1
0
1
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1


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