Number System 2003
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NUMBER SYSTEM Binary 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111
Decimal 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Binary 000 001 010 011 100 101 110 111 000 001 010 011 100 101 110 111
Decimal 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
DECIMAL TO BINARY CONVERSION
(1 56) 10 = (X ) 2 2)156 0 2)78 0 2)39 1 2)19 1 2)9 1 2)4 0 2)2 0 2)1 1 2)0 0
15610 = 100111002
FLOATING POINT DECIMAL TO BINARY CONVERSION
(1 56.75) 10 = (X ) 2 2)156 0 2)78 0 2)39 1 2)19 1 2)9 1 2)4 0 2)2 0 2)1 1 2)0 0
.75 * 2= 1.50 TAKE
1 .50 * 2 = 1.00 TAKE 1
156.7510 = 10011100.112
BINARY TO DECIMAL CONVERSION
(1 0011100) 2 = (X ) 10 1 * 27 + 0* 26 + 0 * 25 +1 * 24+1 * 23+ 1 * 22+ 0 *21 +0* 20 =
128+0+0+16+8+4+0+0
=156
100111002 =15610
BINARY TO FLOATING POINT DECIMAL CONVERSION
(1 0011100.1 1) 2= (X) 10 1 * 27 + 0* 26 + 0 * 25 +1 * 24+1 * 23+ 1 * 22+ 0 *21 +0* 20 =
128+0+0+16+8+4+0+0
=156 1*2-1+1*2-2 =.5+.25 =.75
10011100.112 =156.7510
DECIMAL TO OCTAL CONVERSION
(5 358) 10= (X ) 8 535810=101001110111012 101001110111012 = 10|100|111|011|101 =247358
535810 =247358
OCTAL TO DECIMALCONVERSION
(5 358) 8 = (X ) 10 247358 = 10|100|111|011|101= 101001110111012 101001110111012 = 535810
247358 = 535810
DECIMAL TO HEXADECIMAL CONVERSION
(5 358) 10= (X ) 16 535810=101001110111012 101001110111012 =0010 = 29DD16
1001
1101
1101
535810 = 29DD16
HEXADECIMAL TO DECIMAL CONVERSION
(2 9DD) 16 = (X ) 10 29DD16 = 0010 1001 101001110111012
1101
1101 =
01001110111012 = 535810
29DD16 = 535810
Decimal 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Binary 000 001 010 011 100 101 110 111 000 001 010 011 100 101 110 111
Decimal 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
DECIMAL TO BINARY CONVERSION
(1 56) 10 = (X ) 2 2)156 0 2)78 0 2)39 1 2)19 1 2)9 1 2)4 0 2)2 0 2)1 1 2)0 0
15610 = 100111002
FLOATING POINT DECIMAL TO BINARY CONVERSION
(1 56.75) 10 = (X ) 2 2)156 0 2)78 0 2)39 1 2)19 1 2)9 1 2)4 0 2)2 0 2)1 1 2)0 0
.75 * 2= 1.50 TAKE
1 .50 * 2 = 1.00 TAKE 1
156.7510 = 10011100.112
BINARY TO DECIMAL CONVERSION
(1 0011100) 2 = (X ) 10 1 * 27 + 0* 26 + 0 * 25 +1 * 24+1 * 23+ 1 * 22+ 0 *21 +0* 20 =
128+0+0+16+8+4+0+0
=156
100111002 =15610
BINARY TO FLOATING POINT DECIMAL CONVERSION
(1 0011100.1 1) 2= (X) 10 1 * 27 + 0* 26 + 0 * 25 +1 * 24+1 * 23+ 1 * 22+ 0 *21 +0* 20 =
128+0+0+16+8+4+0+0
=156 1*2-1+1*2-2 =.5+.25 =.75
10011100.112 =156.7510
DECIMAL TO OCTAL CONVERSION
(5 358) 10= (X ) 8 535810=101001110111012 101001110111012 = 10|100|111|011|101 =247358
535810 =247358
OCTAL TO DECIMALCONVERSION
(5 358) 8 = (X ) 10 247358 = 10|100|111|011|101= 101001110111012 101001110111012 = 535810
247358 = 535810
DECIMAL TO HEXADECIMAL CONVERSION
(5 358) 10= (X ) 16 535810=101001110111012 101001110111012 =0010 = 29DD16
1001
1101
1101
535810 = 29DD16
HEXADECIMAL TO DECIMAL CONVERSION
(2 9DD) 16 = (X ) 10 29DD16 = 0010 1001 101001110111012
1101
1101 =
01001110111012 = 535810
29DD16 = 535810
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