Question

Computer science digital logics

Convert the following as specified DEC in hex to its decimal DEC in hex to BCD Convert (1001011101010010) in BCD to OCTAL Convert (7643)_8 to Hex.

Answer 1

1(a)

DEC in hex to its decimal

(DEC)₁₆ = ( )₁₀

= D*16²   +   E*16¹   + C*16⁰

= 13*256 + 14*16 + 12*1

= 3328 + 224 +12

= (3564)₁₀

b)

(DEC)₁₆ to BCD

(DEC)₁₆ = (3564)₁₀

(3564)₁₀ to BCD

3= 0011

5 = 0101

6 = 0110

4= 0100

BCD = 0011 0101 0110 0100

2(a)

1001 0111 0101 0010 BCD to octal

= 1001 =9, 0111=7, 0101=5, 0010 =2 from BCD to decimal =(9752)₁₀

= (9752)₁₀    to octal

                                             remainders

8|9752

8|1219                                     0

8|152                                       3

8|19                                         0

8|2                                           3

|0                                             2

taking remainders in reverse

=(23030)₈

b)

(7643)₈     to hex

7 = 111

6=110

4=100

3= 011

three bits for octal number

= 111 110 100 011

taking 4 bits to denote hexadecimal number

= 1111 1010 0011

= (FA3)     in hexadecimal

=(FA3)₁₆