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Step of 6 2.018E The possible radices for below arithmetic operations are as follows, (a) Arithmetic operation, 1234+5432=6666 The greatest number used in the above equation is 6. Therefore the above arithmetic operation is possible in radices more than 6, example radix 7 (terms are between 0 and 6) & above. Step of 6 (b) Arithmetic operation, 41 3 Let us take radix as X. In radices, a string of digits such as d₁d₂d₃ are denotes the decimal as whereas X is the radix of the system. Therefore the above arithmetic operation can be written as follows. 4x+1 3 Solve the equation as follows. 4x+1=3(x+3) 4x+1=3x+9 4x+1-3x-9=0 x-8=0 x=8 Thus the given arithmetic operation is possible in radix 8 or octal representation. Step of 6 (c) Arithmetic operation, The greatest number used in the above equation is 3. Therefore the above arithmetic operation is possible in radices more than 3, example radix 4(terms are between 0 and 3) & above. Step of 6 (d) Arithmetic operation, 23+44+14+32=223 Let us take radix as X. In radices, a string of digits such as d₁d₂d₃ are denotes the decimal as whereas X is the radix of the system. Therefore the above arithmetic operation can be written as follows, Solve the equation as follows. x²-4x-5=0 (x+1)(x-5)=0 Radix must be positive. Therefore x=5. Thus the given arithmetic operation is possible in radix 5. Step of 6 (e) Arithmetic operation, 302 20 Let us take radix as X. In radices, a string of digits such as d₁d₂d₃ are denotes the decimal as whereas X is the radix of the system. Therefore the given arithmetic operation can be written as follows, 2x x Solve the equation as follows. 2x x Cancelling X in denominator on both sides, x²-4x=0 or 4 Radix must be greater than 0. Therefore x=4 Thus the given arithmetic operation is possible in radix 4. Step of 6 (f) Arithmetic operation, Let us take radix as X. In radices, a string of digits such as are denotes the decimal as whereas X is the radix of the system. Therefore the given arithmetic operation can be written as follows, Solving the equation as follows, Squaring the equation on both sides, (4x+1)=25 4x+1-25=0 4x-24=0 24 4 x=6 Thus the given arithmetic operation is possible in radix 6.