What is the decimal equivalent of the binary value 1001 1111 1001 0101 when treated as a 16-bit signed magnitude value? What is the decimal equivalent of +7948 when written as a 16-bit unsigned value?
The decimal equivalent of the binary value 1001 1111 1001 0101 when treated as a 16-bit signed magnitude value is -15637. The decimal equivalent of +7948 when written as a 16-bit unsigned value is 1110 0110 1100.
Decimal Equivalent of Binary Value as 16-bit Signed Magnitude
The binary value 1001 1111 1001 0101 when treated as a 16-bit signed magnitude value is interpreted as follows:
- The leftmost bit is 1, indicating a negative sign.
- The remaining bits (001 1111 1001 0101) represent the magnitude of the number.
Converting the magnitude to decimal:
001 1111 1001 0101 = 2^13 + 2^12 + 2^11 + 2^10 + 2^9 + 2^7 + 2^5 + 2^2 + 2^0
= 8192 + 4096 + 2048 + 1024 + 512 + 128 + 32 + 4 + 1
= 15637
Therefore, the decimal equivalent of the binary value 1001 1111 1001 0101 as a 16-bit signed magnitude value is -15637.
Decimal Equivalent of +7948 as 16-bit Unsigned Value
To write +7948 as a 16-bit unsigned value, we convert the decimal value to binary:
+7948 = 1 1110 0110 1100
Therefore, the decimal equivalent of the binary value +7948 as a 16-bit unsigned value is 1110 0110 1100.