Question

1. Complete the following table:

Signed two’s complement binary integers (where m=# of bits)

Using m bits	Minimum Value that can be represented expressed in base 2	Minimum Value that can be represented expressed in base 10	Maximum Value that can be represented expressed in base 2	Maximum Value that can be represented expressed in base 10
7
12
15

Answer 1

Please check out the solution of the given problem... for any doubt, please let me know...

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The range formula for 2's complement is [ -2^n-1 to +2^n-1 -1 ] where n is the number of bits..

FOR 7 BIT:

The range of integers in 2's complement form in 7 bits is [ -2^7-1 to +2^7-1 - 1 ]

so minimum number can be represented is ( - 2⁶ )₁₀ => (-64)₁₀ or (1111111)₂

maximum number can be represented is ( + 2⁶ - 1)₁₀ => (+63 )₁₀ or (0111111)₂

FOR 12 BIT:

The range of integers in 2's complement form in 12 bits is [ -2^12-1 to +2^12-1 - 1 ]

so minimum number can be represented is ( - 2¹¹ )₁₀ => ( - 2048 )₁₀ or (111111111111)₂

maximum number can be represented is ( + 2¹¹ - 1)₁₀ => (+2047 )₁₀ or (011111111111)₂

FOR 15 BIT:

The rnge of integers in 2's complement form in 15 bits is [ -2^15-1 to +2^15-1 - 1 ]

so minimum number can be represented is ( - 2¹⁴ )₁₀ => ( - 16384)₁₀ or (111111111111111)₂

maximum number can be represented is ( + 2¹⁴ - 1)₁₀ => (+16383 )₁₀ or (011111111111111)₂

so the table will be...

Bits	Minimum Value that can be represented expressed in base 2	Minimum Value that can be represented expressed in base 10	Maximum Value that can be represented expressed in base 2	Maximum Value that can be represented expressed in base 10
7	(1111111)2	(-64)10	(0111111)2	(+63 )10
12	(111111111111)2	( - 2048 )10	(011111111111)2	(+2047 )10
15	(111111111111111)2	( - 16384)10	(011111111111111)2	(+16383 )10