Do the following Conversions Convert the following binary nu

Do the following Conversions

Convert the following binary numbers to denary numbers: (a) 000011, (b) 111111, (c) 001101.

Convert the following denary numbers to binary numbers: (a) 100, (b) 146, (c) 255.

Convert the following hexadecimal numbers to denary numbers: (a) 9F, (b) D53, (c) 67C.

Convert the following denary numbers to hexadecimal numbers: (a) 14, (b) 81, (c) 2562.

Convert the following hexadecimal numbers to binary numbers: (a) E, (b) 1D, (c) A65.

Convert the following octal numbers to denary numbers: (a) 372, (b) 14, (c) 2540.

Convert the following denary numbers to octal numbers: (a) 20, (b) 265, (c) 400.

Convert the following octal numbers to binary numbers: (a) 270, (b) 102, (c) 673

Solution

To convert binary number to denary number

000011

= 1*1 + 1*2 + 0*4 + 0*8 + 0*16 + 0*32 = 3

111111

= 1*1 + 1*2 + 1*4 + 1*8 + 1*16 + 1*32 = 63

001101

= 1*1 + 0*2 + 1*4 + 1*8 + 0*16 + 0*32 = 13

denary numbers to binary numbers

100

100<128 insert 0

As 100>64 insert 1 and remaining value = 100-64 = 36

As 36>32 insert 1 and remaining value = 36-32 = 4

AS 4<16 insert 0

As 4<8 insert 0

AS 4= 4 insert 1 remaining value = 0

So the binary number of 100 is 01100100

146

AS 146 > 128 inser 1 remaining value = 146-128 = 18

AS 18<64 insert 0

As 18<32 insert 0

As 18>16 inser 1 remaining value = 18-16 = 2

As 2<8 insert 0

As 2<4 insert 0

As 2=2 insert 1 remaining value = 0

The binary number of 146 is 10010010

255

As 255 >128 insert 1 remaining value = 255-128=127

As 127>64 insert 1 remaining value = 127-64=63

As 63>32 insert 1 remaining value = 63-32 =31

As 31>16 insert 1 remaining value = 31-16=15

As 15>8 insert 1 remaining value =15-8=7

As 7>4 insert 1 remaining value = 7-4 = 3

As 3>2 insert1 remaining value = 3-2 =1

As 1=1 insert 1

the binary form of 255 = 11111111

hexadecimal numbers to denary numbers

9F

=F*1 + 9 *16

=15*1 +9 *16

=159

D53

= 3*1 + 5*16 + D *256

=3*1 + 5*16 + 13*256

=3411

67C

=C*1 +7*16 + 6*256

=12*1 + 7*16 + 6*256

=1660

denary numbers to hexadecimal numbers

14

= E

81

first convert to binary

81<128 insert 0

81>64 inser 1 remaining = 81-64 = 17

17<32 insert 0

17>16 insert 1 remaining 1

1<8 insert 0, 1<4 insert 0, 1<2 insert 0

1=1 insert 1

binary number is 0101 0001

make the binary into 2 parts 0101 and 0001

0101 = 5 and 0001 =1

the hexadecimal number of 81 is 51

2562

convert it to binary

2562>2048 insert 1 remaining value = 2562-2048 = 514

514>512 insert 1 remaining value = 2

2 = 2 insert 1 remaining value = 0

The binary form is 1010 0000 0010

the binary number is divided into three parts

1010 = 10 = A

0000 = 0 = 0

0010 = 2 = 2

The hexadecimal number of 2562 is A02

hexadecimal numbers to binary numbers

E

denary number of E = 14

binary number of 14 = 1110

1D

binary number of 1 =0001

denary number of D = 13

binary number of 13 = 1101

The binary form of 1D = 00011101

A65

denary number of A = 10

binary number of 10 = 1010

binary number of 6 = 0110

binary number of 5 = 0101

The binary number of A65 =101001100101

128	64	32	16	8	4	2	1
0	1	1	0	0	1	0	0