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Key Takeaways

Essential concepts, definitions, and common exam pitfalls for Chapter 10.1: Standard Logic Gate Symbols.

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STATE / IDENTIFY

Brief, factual answer — no explanation needed

1State the denary value of binary 1010
  • 10  (8 + 2)
2Identify the base of the hexadecimal number system
  • 16  (digits 0–9 and A–F)
3State how many bits are in a nibble
  • 4 bits
4Identify the largest denary value that can be held in an 8-bit register
  • 255  (binary 11111111)
5State the effect of one logical left shift on a binary number
  • The value is multiplied by 2

DESCRIBE

Say what happens or how it works (what / how)

1Describe how to convert denary to hexadecimal
  • Divide repeatedly by 16, recording the remainders
  • Read the remainders from bottom to top
  • Alternatively: convert to binary, then split into nibbles
2Describe how to convert binary to hexadecimal
  • Split the binary into groups of 4 bits starting from the right
  • Pad the leftmost group with leading 0s if needed
  • Convert each nibble to its hex digit (e.g. 1101 → D)
3Describe how two's complement represents negative numbers
  • The leftmost bit acts as a sign bit: 0 = positive, 1 = negative
  • The leftmost bit holds the value −128 in an 8-bit register
  • Range is −128 to +127
4Describe what happens to bits shifted out of an 8-bit register
  • Bits shifted beyond the register are lost
  • Zeros are shifted in at the opposite end
  • If a 1 is lost the value becomes incorrect
5Describe the structure of a MAC address
  • 48 bits usually written as 6 hexadecimal pairs, e.g. 00-1C-B3-4F-25-FE
  • First half identifies the manufacturer
  • Second half is the device serial number

EXPLAIN

Give reasons — say why something happens

1Explain why overflow occurs when adding two 8-bit binary integers
  • If the sum is greater than 255 a 9th bit is needed
  • Only 8 bits are available so the carry is lost
  • The stored result is incorrect — this is an overflow error
2Explain why hexadecimal is used as a shorthand for binary
  • One hex digit represents exactly 4 bits (one nibble)
  • Hex values are much shorter than the equivalent binary
  • Easier for humans to read, remember and copy with fewer errors
3Explain why computers use binary to represent all data
  • Computer hardware has millions of tiny switches with two states
  • Switch on = 1, switch off = 0
  • Logic gates process the 1s and 0s and values are stored in registers
4Explain why repeated left shifts can give an incorrect result
  • Each left shift multiplies the value by 2
  • After several shifts the value exceeds 255 (8-bit maximum)
  • The most significant bits are lost so the stored value is wrong
5Explain why two's complement is used for signed integers
  • It can represent both positive and negative integers
  • There is only one representation of zero
  • The same adder hardware can perform subtraction

EVALUATE / DISCUSS

Weigh up pros and cons with a justified conclusion

1Discuss why programmers prefer to read memory dumps in hexadecimal rather than binary
  • Hex is far shorter — 2 hex digits per byte vs 8 bits
  • Easier to identify values and spot errors when debugging
  • Each hex digit still maps directly to 4 bits so no information is lost
  • Binary is what the hardware uses, but hex is a human-friendly view
2Evaluate the effect of performing several left shifts on an 8-bit register
  • Each shift multiplies the value by 2 (shift n places = ×2ⁿ)
  • Only a limited number of shifts is possible before the value exceeds 255
  • Once the MSB is lost the stored value is incorrect
  • The register size places a hard limit on the calculation
3Discuss whether displaying error codes in hexadecimal is beneficial
  • Error codes refer to memory locations and are generated automatically
  • Hex keeps codes short and readable compared to long binary strings
  • Programmers can interpret locations quickly and spot errors more easily
  • The computer still processes the value in binary — hex is presentation only
4Discuss the impact of using a 16-bit register instead of an 8-bit register
  • 16 bits store 65 536 values (0–65535) vs only 256 (0–255)
  • Larger calculations can be performed before overflow occurs
  • Fewer overflow errors, but more bits are needed to store each value
  • Conversions and transmission involve more bits per number
5Discuss the limitations of 8-bit two's complement
  • Only stores −128 to +127 — a narrow range
  • Values outside the range cause overflow
  • More bits (16/32) give a larger range at the cost of memory
  • Choice of register size depends on the values the program must handle