Binary equality is only one possible comparison. An electronic selector may need to know whether a requested value is below, equal to or above a limit. Build a four-bit magnitude comparator with eight switches and three indicators. Change the most significant bit and watch it outweigh every lower bit; then discover why the cascade inputs must be wired even when there is only one chip.
This exact-part circuit and its logical oracle are prepared for a low-voltage bench experiment. No physical assembly, waveform measurement or target firmware execution is claimed. The ordering map is calculated from valid settled input words; it is not an oscilloscope trace.
A magnitude comparator decides which of two numbers is larger. The Texas Instruments CD74HC85E compares two four-bit words, A and B, and provides three separate outputs: A less than B, A equal to B and A greater than B. A bit is a binary digit, zero or one. In this unsigned experiment, the four positions have weights 1, 2, 4 and 8. The most significant bit has the largest weight; a difference there settles the comparison regardless of the lower positions.
This is a digital comparison of encoded numbers, not an analog voltage comparator. Four HIGH inputs encode fifteen, rather than a measured 15 V. It is also not a subtractor: the outputs give a relation, not a numerical difference. The chip does not remember an old word or decide when moving switches constitute a completed update.
Cascade inputs carry the comparison result of a less significant section when several chips form a wider comparator. For a standalone section, the imaginary lower section is equal: set the equality input HIGH and the less/greater inputs LOW. When local A and B differ, their comparison decides the output; when they match, the lower-section result matters. These inputs are functional signals, not spare pins.
Use TI CD74HC85E, N package, a 16-pin plastic dual in-line package (PDIP); a regulated 4.5 V source with a 20 mA current limit; a 100 nF ceramic bypass; eight single-pole double-throw (SPDT) selectors; eight 1 kΩ series resistors; eight 10 kΩ pulldowns; and three red light-emitting diodes (LEDs), each with its own 3.3 kΩ resistor. Ω denotes ohm, kΩ one thousand ohms, nF nanofarad, V volt and mA milliampere. Use resistors rated at least 0.125 W.
| Group | Physical pins | Meaning |
|---|---|---|
| A0,A1,A2,A3 | 10,12,13,15 | Weights 1, 2, 4, 8 |
| B0,B1,B2,B3 | 9,11,14,1 | Weights 1, 2, 4, 8 |
| Lower less/equal/greater | 2,3,4 | Ground, +4.5 V, ground for standalone use |
| Greater/equal/less outputs | 5,6,7 | Separate active-HIGH indications |
| Supply and return | 16,8 | +4.5 V, ground; 100 nF directly between them |
Read the top-view notch and pin-one drawing before insertion. The exact HC device operates at 2–6 V; this experiment chooses 4.5 V so its published 4.5 V input limits apply. A valid HIGH is at least 3.15 V and a valid LOW at most 1.35 V. A voltage between these limits is undefined. The 7 V absolute supply boundary is a stress limit, not a working supply. CD74HCT85 is a different input-level variant; this is not a permission to substitute by similar name.
Disconnect power before wiring. Each selector chooses ground or +4.5 V; its common contact feeds the relevant input through 1 kΩ. Add 10 kΩ from the chip input to ground. This defines an open contact as LOW and limits accidental contact current. At HIGH, that cell forms a divider: 4.5 × 10/11 ≈ 4.09 V, above the required 3.15 V. Check real levels if the result is unexpected.
Each output feeds its own 3.3 kΩ resistor, then an LED anode; the cathode returns to ground. With an illustrative 1.6 V forward drop, its load is approximately (4.5 − 1.6)/3300 ≈ 0.88 mA. Brightness is not a voltage measurement; the forward drop varies. Do not join the three push-pull outputs together. A valid settled comparison normally asserts one result, but shorting outputs is not a way to combine their information.
Keep every input defined and keep the bypass close to the supply pins. Raw HC inputs need sufficiently fast transitions. Do not add a large capacitor to an input as a casual switch-debounce fix. This experiment records settled words after contact movement stops. A clocked receiving circuit and qualified conditioning are needed for a design that must capture a changing word at a defined instant.
Use the blank observation sheet. Sequentially moving four selectors passes through intermediate words. A briefly different output can be a legitimate comparison of one of those words, not a faulty arithmetic unit. Separately, internal path delays can produce short transient results. The static map does not promise that every output change is glitch-free.
The Python 3.11 program runs on a host computer and needs no microcontroller. It compares valid four-bit words and accepts a valid one-hot lower result: one of the three result signals is asserted. Unknown inputs return None; unsupported cascade combinations are rejected rather than presented as a model of illegal hardware states. The optional eight-bit function compares lower and upper nibbles, where a nibble is four bits. It demonstrates significance without claiming a second chip was wired.
"""CD74HC85E valid-state logical oracle; not a propagation/silicon model."""
def word(value, maximum=15):
if type(value) is not int or not 0 <= value <= maximum:
raise ValueError("word outside the declared unsigned range")
return value
def compare4(a, b, lower=(0, 1, 0)):
"""Output tuple: (A<B, A=B, A>B). Only valid one-hot lower states modelled."""
lower = tuple(lower)
if len(lower) != 3 or any(type(x) is not int or x not in (0, 1) for x in lower):
raise ValueError("lower state needs three integer bits")
if sum(lower) != 1:
raise ValueError("this oracle refuses unsupported cascade input combinations")
if a is not None:
word(a)
if b is not None:
word(b)
if a is None or b is None:
return None
if a < b:
return (1, 0, 0)
if a > b:
return (0, 0, 1)
return lower
def compare8(a, b):
word(a, 255); word(b, 255)
low = compare4(a & 15, b & 15)
return compare4(a >> 4, b >> 4, low)
if __name__ == "__main__":
print("A,B,less,equal,greater")
for a, b in [(0, 0), (7, 8), (8, 7), (15, 15), (1, 2)]:
print(a, b, *compare4(a, b), sep=",")
Host checks execute all 256 four-bit comparisons and all 65,536 eight-bit comparisons, as cases within named behavior groups. They also test equal-section forwarding, unknowns, invalid values and unsigned interpretation. Those checks verify the supplied logic, not package continuity, output voltage or a physical propagation delay. The bench sheet intentionally contains no synthetic readings.
If a weight behaves backwards, inspect the A/B pin assignments: their physical order is not simply A0,A1,A2,A3 down one side. If equal is always off, verify cascade pin 3 is HIGH and pins 2/4 are LOW. If more than one LED appears on, measure settled output levels and inspect shorts or changing inputs before interpreting the display. A reversed LED can hide a correct output.
The chip interprets the bit pattern in the intended unsigned ordering. It does not know a program's signed-number convention. An output relation also says nothing about whether the input came from an accurate sensor or a complete received message. Separate the encoding, update timing and comparison result in the experiment record.
In four-bit two's-complement arithmetic, 1000 represents −8. Why does this circuit say 1000 is greater than 0111?
The circuit sees unsigned weights 8, 4, 2, 1, so it compares 8 with 7. Two's complement is a signed encoding convention that changes the significance of the top bit. A signed comparator needs that convention handled explicitly; changing the label on a wire does not change this unsigned experiment.
TI CD74HC85 SCHS136F, February 2022 supplies exact pins, cascade functions, operating levels and timing conditions. Current TI documentation was checked October 20, 2026; no separate applicable errata sheet surfaced, which is not proof of absence. The Python 3.11 documentation supports the host workflow. Continue with the electronics course.