SM is sign and magnitude R is radix DR is diminished radix C

SM is \"sign and magnitude\"

R is \"radix\"

DR is \"diminished radix\"

Convert the following number into the requested representation (SM rightarrow \"sign + magnitude\"; DR rightarrow \"diminished radix\"; R rightarrow \"radius\") SM(100111000101)_2 = SM(?)_10, R(?)_2, DR(?)_2, SM(>)_16, R(?)_8, DR(?)_8

Solution

Ans) In sign magnitude form left most bit is 1 it is negative number

SM(100111 000101)₂=SM(-(2⁸+2⁷+2⁶+2²+2⁰))₁₀=SM(-453)₁₀

Radix compliment i.e 2\'s compliment her is 1\'s compliment +1=011000 111010+1=011000 111011

R(011000 111011)₂

DR-of 2 means 1\'s compliment i.e inverting each bit as already done above for 2\'s compliment

DR(011000 111010)₂

SM(9C5)₁₆ by grouping each 4 bits in base 2     SM(1001 1100 0101)₂

For SM()₈ group 3 bits at time find its radix 8 equivalent

SM(100 111 000 101)₂

i.eSM(4705)₈

For R-8 ---7\'s compliment +1 i.e substract number from 7777

7777

4705

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3072 +1=3073

so R(3073)₈

and DR(3072)₈  7\'s compliment obtained above