The access system for a sports centre uses the binary subtraction shown in Fig. 1. A staff member has 01100010 credits, and 00011111 credits are used to boo...
Question 1 Report
The access system for a sports centre uses the binary subtraction shown in Fig. 1. A staff member has 01100010 credits, and 00011111 credits are used to book a court.
(a) Give the 8-bit result of the subtraction. [2]
(b) State the denary value of the result. [1]
(c) State the number of credits used. [1]
Fig. 1 shows an 8-bit register in a portable music player. A programmer needs to multiply the binary number by 2 using a shift operation. The value is currently held in the register.
(a) Give the value after a logical left shift by one position. [2]
(b) State the denary value after the shift. [1]
(c) State the effect on the leftmost bit if another left shift is performed. [1]
Answer Details
Sports-centre credits
- \[01100010_2-00011111_2=01000011_2\]
[2] - \(01000011_2=64+2+1=67\). [1]
- The number of credits used is 31, since \(00011111_2=16+8+4+2+1=31\). [1]
Music-player register
- A logical left shift by one gives:
\[00110101 \rightarrow 01101010\]
[2] - \(01101010_2=64+32+8+2=106\). [1]
- If another left shift is performed, the leftmost bit is discarded or lost from the fixed-size register. [1]
A left shift normally multiplies an unsigned value by 2 only while no significant bit is lost.
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