Fig. 1 shows a programmer checking a 4-bit signed binary number in two's complement. The number is stored by a small network device that records a fall in s...
Question 1 Report
Fig. 1 shows a programmer checking a 4-bit signed binary number in two's complement. The number is stored by a small network device that records a fall in signal level.
(a) Give the denary value of 1101 as a two's complement number. [2]
(b) State the binary number that represents positive 5 in 4-bit two's complement. [1]
(c) State the range of denary values possible with 4 bits in two's complement. [1]
Answer Details
- Because the leading bit is 1, \(1101\) is negative in 4-bit two's complement. Invert: \(0010\); add 1: \(0011\), which is 3. Therefore the value is \(-3\). [2]
- Positive 5 in 4-bit binary is \(0101\). [1]
- With \(n\) bits in two's complement, the range is \(-2^{n-1}\) to \(2^{n-1}-1\). For 4 bits, this is \(-8\) to \(+7\). [1]
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